tag:blogger.com,1999:blog-81097221567684096552024-03-13T20:07:07.460-07:00NUMERICAL METHODS FOR ENGINEERINGMEIBY ALEJANDRA TOLEDO ARIZAhttp://www.blogger.com/profile/03585855169767775681noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-8109722156768409655.post-63931074780650050442010-07-20T15:00:00.000-07:002010-07-20T15:43:19.223-07:00ITERATIVE METHODS FOR SOLUTION OF SYSTEMS OF LINEAR EQUATIONS <div style="text-align: center;"><span style="font-weight: bold; color: rgb(153, 51, 153); font-family: arial;" id="result_box" class="short_text"><span style="" title="">
<br />ITERATIVE METHODS FOR SOLUTION OF SYSTEMS OF LINEAR EQUATIONS
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margin:70.85pt 3.0cm 70.85pt 3.0cm; mso-header-margin:35.4pt; mso-footer-margin:35.4pt; mso-paper-source:0;} div.WordSection1 {page:WordSection1;} --> </style><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabla normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin-top:0cm; mso-para-margin-right:0cm; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0cm; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin;} </style> <![endif]--> <p style="text-align: justify; font-family: arial;" class="MsoNormal"><span class="mediumtext"><span style="" lang="EN-US">In general, these methods are based on fixed point method and the process is iterated so substitute in a formula.</span><o:p></o:p></span></p><div style="font-family: arial;"> </div><p style="text-align: left; font-family: arial;" class="MsoNormal"><span class="longtext"><span style="" lang="EN-US">Iterative methods compared with direct, we do not guarantee a better approach, however, are more efficient when working with large matrices.</span></span><span style="" lang="EN-US">
<br /></span></p><div style="text-align: justify;"><span id="result_box" class="long_text"><span style="" title="">In computational mathematics, is an iterative method to solve a problem (as an equation or a system of equations) by successive approximations to the solution, starting from an initial estimate. </span><span style="background-color: rgb(255, 255, 255);" title="">This approach contrasts with the direct methods, which attempt to solve the problem once (like solving a system of equations Ax = b by finding the inverse of the matrix A). </span><span style="background-color: rgb(255, 255, 255);" title="">Iterative methods are useful for solving problems involving a large number of variables (sometimes in the millions), where direct methods would be prohibitively expensive even with better computer power available.</span></span></div><p style="text-align: left; font-family: arial;" class="MsoNormal">
<br /></p><div style="text-align: left; font-family: arial;"> </div><ul style="text-align: left; font-family: arial;"><li><span style="font-weight: bold;" class="shorttext">JACOBI METHOD</span><span class="longtext"><span style="" lang="EN-US"><o:p></o:p></span></span></li></ul><div style="text-align: left; font-family: arial;"> </div><p style="text-align: justify; font-family: arial;" class="MsoNormal"><span class="longtext"><span style="background: white none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" lang="EN-US">The basis of the method is to construct a convergent sequence defined iteratively. </span><span title="El límite de esta sucesión es precisamente la solución del sistema." onmouseover="this.style.backgroundColor='#ebeff9'" onmouseout="this.style.backgroundColor='#fff'">The limit of this sequence is precisely the solution of the system. </span><span title="A efectos prácticos si el algoritmo se detiene después de un número finito de pasos se llega a una aproximación al valor de x de la solución del sistema." onmouseover="this.style.backgroundColor='#ebeff9'" onmouseout="this.style.backgroundColor='#fff'">For practical purposes if the algorithm stops after a finite number of steps leads to an approximation of the value of x in the solution of the system. </span></span><span style="background: white none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" lang="EN-US">
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<br /><span title="La sucesión se construye descomponiendo la matriz del sistema \mathbf{A} en la forma siguiente:" onmouseover="this.style.backgroundColor='#ebeff9'" onmouseout="this.style.backgroundColor='#fff'">
<br /></span></span><span style="" lang="EN-US"></span></p><div style="font-family: arial;"> </div><ul style="text-align: left; font-weight: bold; font-family: arial;"><li><span class="longtext"><span style="" lang="EN-US">GAUSS SEIDEL METHOD</span></span></li></ul><p style="text-align: left; font-family: arial;" class="MsoNormal"><span style="" lang="EN-US">
<br /><span class="longtext"></span><span title="">The methods of Gauss and Cholesky methods are part of direct or </span><span class="longtext"></span><span title="">finite. </span><span style="background: white none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span title="">After a number of operations nito, in the absence of errors </span></span><span style="background: white none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span class="longtext"></span><span title="">rounding, we get x solution of the system Ax = b. </span><span class="longtext"></span><span title="">The Gauss-Seidel method is part of the so-called indirect methods or </span></span><span class="longtext"></span><span title="">iterative. </span><span style="background: white none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span title="">They start with x0 = (x01, X02,:::; x0 n), an approximation </span></span><span style="background: white none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span class="longtext"></span><span title="">initial solution. </span></span><span title=""></span><span class="longtext">Since x0 is building a new approach of </span><span class="longtext"></span><span style="background: white none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span title="">the solution, x1 = (x11, x12;:::; x1n).</span></span><span style="background: white none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">
<br />
<br /><span class="longtext"> </span><span title="">From built x1 x2 (here the superscript indicates the iteration and does not indicate a power). </span><span title="">So on construye fxkg a sequence of vectors, with the aim, not always guaranteed to quelimk! 1xk = x:</span></span><span class="longtext"></span><span title="">Generally, indirect thods are a good option when the matrix </span><span class="longtext"></span><span style="background: white none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span title="">is very large and dispersed or sparse (sparse), ie when the number of </span></span><span style="background: white none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span title="">onzero elements is small compared to n2, total number of elements </span></span><span class="longtext"></span><span title="">A.</span>
<br />
<br /><span class="longtext"></span><span style="background: white none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span title="">In these cases you must use an appropriate data structure </span></span><span style="background: white none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span class="longtext"></span><span title="">lets you store only the nonzero elements. </span><span class="longtext"></span><span title="">In each iteration of the Gauss-Seidel method, there are n subiteraciones. </span></span><span title=""></span><span class="longtext">In </span><span class="longtext"></span><span style="background: white none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span title="">ca first subiteracion be amended only x1. </span><span title="">The other coordinates x2, </span></span><span style="background: white none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span class="longtext"></span><span title="">x3, ..., xn are not modified can.</span></span></span><o:p></o:p></p>
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<br /><div style="text-align: left; font-family: arial; font-style: italic;">fuente
<br /></div><address style="font-family: arial; font-style: italic;"> </address><ul style="text-align: left; font-family: arial;"><li style="font-style: italic;">Wladimiro Diaz Villanueva 1998-05-11</li><li style="font-style: italic;"><a href="http://www.math-linux.com/spip.php?article49" class="external text" title="http://www.math-linux.com/spip.php?article49" rel="nofollow">Método de Jacobi de www.math-linux.com</a></li><li><a href="http://mathworld.wolfram.com/JacobiMethod.html" class="external text" title="http://mathworld.wolfram.com/JacobiMethod.html" rel="nofollow"><span style="font-style: italic;">Método de Jacobi en el mundo de la matemática</span>s</a></li></ul><address> </address></div>MEIBY ALEJANDRA TOLEDO ARIZAhttp://www.blogger.com/profile/03585855169767775681noreply@blogger.com2tag:blogger.com,1999:blog-8109722156768409655.post-66210866482264206972010-07-20T13:36:00.000-07:002010-07-20T16:03:03.575-07:00DIRECT METHOD FOR SOLVING SYSTEMS OF LINEAR EQUATIONS<span id="result_box" class="short_text" style="font-family:arial;"><span style="" title=""><br /></span></span><div style="text-align: center;font-family:arial;"><span style="font-weight: bold; color: rgb(153, 51, 153);font-size:100%;" id="result_box" class="short_text" ><span style="" title="">DIRECT METHOD FOR SOLVING SYSTEMS OF LINEAR EQUATIONS</span></span><br /><span id="result_box" class="short_text"><span style="" title=""></span></span></div><span id="result_box" class="short_text" style="font-family:arial;"><span style="" title=""><br /></span></span> <cite style="font-style: normal; font-family: arial;" id="CITAREFShen_Kangshen_et_al._.28ed..291999"></cite><br /><div style="text-align: justify;font-family:arial;"><span id="result_box" class="long_text"><span style="" title="">In this lesson we study the solution of a Cramer system Ax = B, which </span></span><span id="result_box" class="long_text"><span style="" title="">mea</span></span><span id="result_box" class="long_text"><span style="" title="">ns that A is ° c</span></span><br /></div><div style="text-align: justify;"><div style="text-align: justify;font-family:arial;"><span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title="">invertible regular or verify ° c or det (A) 6 = 0, using a direct method. </span><span style="background-color: rgb(255, 255, 255);" title="">Since this is any</span></span><br /><span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title="">allowing, in the absence of errors, through a number of steps nito obtain the exact solution.</span></span><br /><span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title="">In property, this does not happen in general because of the inevitable rounding errors.</span></span><br /></div><br /><br /><ul style="font-weight: bold;font-family:arial;"><li><span style="color: rgb(102, 51, 102);" id="result_box" class="short_text"><span style="" title="">Gauss- Jordan Elimination</span></span><cite style="font-style: normal;" id="CITAREFShen_Kangshen_et_al._.28ed..291999"></cite><cite style="font-style: normal;" id="CITAREFOtto_Bretscher2005"></cite></li><li><br /><span style="font-weight: normal;" id="result_box" class="long_text"><span style="" title="">In mathematics, Gaussian elimination, Gaussian elimination or Gauss-Jordan elimination, so named because Carl Friedrich Gauss and Wilhelm Jordan, are linear algebra algorithms to determine the solutions of a system of linear equations, matrices and inverse finding. </span><span style="" title="">A</span></span><span style="font-weight: normal;" id="result_box" class="long_text"><span style="" title="">system of equations is solved by the Gauss when their solutions are obtained by reducing an equivalent system given in which each equation has one fewe</span></span><cite style="font-style: normal;" id="CITAREFShen_Kangshen_et_al._.28ed..291999"></cite><span style="font-weight: normal;" id="result_box" class="long_text"><span style="" title="">r variables than the last.</span></span><span style="font-weight: normal;" id="result_box" class="long_text"><span style="" title=""> </span><span title="">When applying this process, the resulting matrix is known as "stagger."</span></span> </li></ul><br /><ul style="font-weight: bold;font-family:arial;"><li style="color: rgb(153, 51, 153);">ALGORITHM GAUSS JORDAN</li><li><br /><span style="font-weight: normal;" id="result_box" class="long_text"><span style="" title="">1. </span><span style="" title="">Go to the far left column is not zero</span></span><cite style="font-style: normal;" id="CITAREFOtto_Bretscher2005"></cite><div style="text-align: justify;"><span style="font-weight: normal;" id="result_box" class="long_text"><span style="" title=""> </span><span title="">2. </span><span style="background-color: rgb(255, 255, 255);" title="">If the first line has a zero in this column, swap it with another that does not have</span></span><br /><span style="font-weight: normal;" id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title=""> </span><span title="">3. </span><span style="background-color: rgb(255, 255, 255);" title="">Then, get below zero this item forward, adding appropriate multiples of row than </span></span><cite style="font-style: normal;"></cite><span style="font-weight: normal;" id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title="">h</span></span><span style="font-weight: normal;" id="result_box" class="long_text"><span title=""> </span></span><span style="font-weight: normal;" id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title="">e row below it</span></span><br /><span style="font-weight: normal;" id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title=""> </span><span title="">4. </span><span style="background-color: rgb(255, 255, 255);" title="">Cover the top ro</span></span><span style="font-weight: normal;" id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title="">w and repeat the above process with the remaining submatrix. </span><span style="background-color: rgb(255, 255, 255);" title="">Repea</span></span><span style="font-weight: normal;" id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title="">t with the rest of the lines (at this point the array is in the form of step)</span></span><cite style="font-style: normal;" id="CITAREFShen_Kangshen_et_al._.28ed..291999"></cite><br /><span style="font-weight: normal;" id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title=""> </span><span title="">5. </span><span style="background-color: rgb(255, 255, 255);" title="">Starting with the last line is not zero, move up: for each row get a 1 up front and introduce zero multiples of this sum for the rows corresponding</span></span><br /><br /><span style="font-weight: normal;" id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title="">An interesting variant of Gaussian elimination is what we call Gauss-Jordan, (du</span></span><span style="font-weight: normal;" id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title="">e to Gauss and Wilhelm Jordan mentioned), this is to be a front for getting the steps 1 to 4 (called direct path) and the time </span><span title="">these completed and will result in the reduced echelon form matrix</span></span><span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title="">.</span></span><cite style="font-style: normal;" id="CITAREFShen_Kangshen_et_al._.28ed..291999"></cite><cite style="font-style: normal;" id="CITAREFOtto_Bretscher2005"></cite></div></li></ul><br /><ul style="font-weight: bold; color: rgb(102, 51, 102); font-family: arial;"><li>LU DESCOMPOSITION<cite style="font-style: normal;" id="CITAREFOtto_Bretscher2005"></cite><cite style="font-style: normal;"></cite></li></ul><span style="background-color: rgb(255, 255, 255);font-family:arial;" title="" >ts name is derived from the English words "Lower" and "Upper", which in Spanish translates as "Bottom" and "Superior." </span><span style="font-family:arial;">Studying the process followed in the LU decomposition is possible to understand why this name, considering how original matrix is decomposed into two triangular </span><cite style="font-style: normal; font-family: arial;" id="CITAREFShen_Kangshen_et_al._.28ed..291999"></cite><cite style="font-style: normal; font-family: arial;" id="CITAREFOtto_Bretscher2005"></cite><ul face="arial" style="font-weight: bold;"><li><div style="text-align: justify;"><div style="text-align: justify;"><span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255); font-weight: normal;" title="">LU decomposition involves only operations on the coefficient matrix [A], providing an efficient means to calculate the inverse matrix or solving systems of linear algebra.</span></span><br /><br /><span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255); font-weight: normal;" title="">First you must obtain the matrix [L] and the matrix [U].</span></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcIcCFiBZ0je7wwzWqnxBi72SEMjviwSGaGL33zyTQc19yRIBU1antMsN2q-f5iQybqqBcjrwPc-Q1t2dF7FlOduCzupQ7vAPxXgGDxbEIyO0xKYXMGHo2qTHJT3ZePouZI1Ji-B-kBZrs/s1600/Image25.gif"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer; width: 257px; height: 197px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcIcCFiBZ0je7wwzWqnxBi72SEMjviwSGaGL33zyTQc19yRIBU1antMsN2q-f5iQybqqBcjrwPc-Q1t2dF7FlOduCzupQ7vAPxXgGDxbEIyO0xKYXMGHo2qTHJT3ZePouZI1Ji-B-kBZrs/s320/Image25.gif" alt="" id="BLOGGER_PHOTO_ID_5496096789320047874" border="0" /></a><cite style="font-style: normal;">.</cite><br /><cite style="font-style: normal;" id="CITAREFShen_Kangshen_et_al._.28ed..291999"></cite><br /><span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255); font-weight: normal;" title="">[L] is a diagonal matrix with numbers less than 1 on </span></span>.<span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255); font-weight: normal;" title="">the diagonal. [U] is an upper diagonal matrix on the diagonal which does not necessarily have to be number one.</span></span><cite style="font-style: normal;" id="CITAREFShen_Kangshen_et_al._.28ed..291999"></cite><br /><br /><span id="result_box" class="long_text"><span style="font-weight: normal;" title="">The first step is to break down or transform [A] [L] and [U], ie to obtain the lower triangular matrix [L] and the upper triangular matrix [U]</span></span><cite style="font-style: normal;"></cite></div></div></li></ul><div style="text-align: justify; font-family: arial;"><cite style="font-style: normal;" id="CITAREFShen_Kangshen_et_al._.28ed..291999"></cite><br /><div style="text-align: center;"><br /><br /><ul style="text-align: left; font-weight: bold; color: rgb(153, 51, 153);"><li><span id="result_box" class="medium_text"><span style="" title="">INVERSE MATRIX</span></span></li></ul><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlvy2dNGu5Fxe_vshuUuPh9Gnor8R0pbr56_LN5ivdyhtvYWPsWPiKystyCCkzdN2YSU0Mf1mMEupi5L6wMY0kB0oiFKUHOkN_kQwk999TwsxICplEtRMXKpU2hwnk4u4wqmrPRF94y6xn/s1600/65.gif"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer; width: 320px; height: 184px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlvy2dNGu5Fxe_vshuUuPh9Gnor8R0pbr56_LN5ivdyhtvYWPsWPiKystyCCkzdN2YSU0Mf1mMEupi5L6wMY0kB0oiFKUHOkN_kQwk999TwsxICplEtRMXKpU2hwnk4u4wqmrPRF94y6xn/s320/65.gif" alt="" id="BLOGGER_PHOTO_ID_5496098034191775362" border="0" /></a><br /><div style="text-align: justify;"><span id="result_box" class="medium_text"><span style="" title="">Is the matrix we get from chang</span></span> <span id="result_box" class="medium_text"><span style="" title="">ing rows by columns. </span><span title="">The transpose of that represented by AT.</span></span></div></div></div><cite style="font-style: normal; font-family: arial;" id="CITAREFShen_Kangshen_et_al._.28ed..291999"></cite><br /><span id="result_box" class="long_text" style="font-family:arial;"><span style="" title="">In mathematics, especially in linear algebra, a square matrix of order n is said to be invertible, nonsingular, nondegenerate or regular if there is another square matrix of order n, called the inverse matrix of A and represented as A-1</span></span><span style="font-family:arial;">matrices.</span><cite style="font-style: normal; font-family: arial;"></cite><br /><br /><br /><span style="font-style: italic;font-family:arial;" >fuente</span><cite style="font-style: normal; font-family: arial;" id="CITAREFShen_Kangshen_et_al._.28ed..291999"><br /><br /></cite><ul style="font-family: arial; font-style: italic;"><li><cite style="font-style: normal;" id="CITAREFShen_Kangshen_et_al._.28ed..291999">Shen Kangshen et al. (ed.) (1999). Nine Chapters of the Mathematical Art, Companion and Commentary, Oxford University Press.</cite> cited by<cite style="font-style: normal;" id="CITAREFOtto_Bretscher2005">Otto Bretscher (2005).</cite></li></ul> <ul style="font-family:arial;"><li><cite style="font-style: normal;"> <span style="font-style: italic;">Linear Algebra and Its Applications, Thomson Brooks/Cole, pp. 46</span></cite></li></ul><br /><br /><br /><img src="file:///C:/DOCUME%7E1/equipo1/CONFIG%7E1/Temp/moz-screenshot-14.jpg" alt="" /></div>MEIBY ALEJANDRA TOLEDO ARIZAhttp://www.blogger.com/profile/03585855169767775681noreply@blogger.com0tag:blogger.com,1999:blog-8109722156768409655.post-46615989253202366512010-05-15T17:13:00.000-07:002010-07-20T16:27:48.943-07:00MATHEMATICAL APPROXIMATION<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTURKmYj-wuwreXQMGa7fq9BzlG7WHP8ze2hqpRyASVy3q4aTv098c5p3vNy-nhmSUqcm3swOFMSYzn010Wzvoj57c9CCluHoJlOdYXScMiI9zI6EvSVGuCMFn8bydCy3FO4JWJsmubtY2/s1600/metodos.jpg"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer; width: 320px; height: 240px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTURKmYj-wuwreXQMGa7fq9BzlG7WHP8ze2hqpRyASVy3q4aTv098c5p3vNy-nhmSUqcm3swOFMSYzn010Wzvoj57c9CCluHoJlOdYXScMiI9zI6EvSVGuCMFn8bydCy3FO4JWJsmubtY2/s320/metodos.jpg" alt="" id="BLOGGER_PHOTO_ID_5496056093644648130" border="0" /></a><br /><div style="text-align: center;"><span style="font-weight: bold; color: rgb(204, 51, 204);font-family:arial;" >MATHEMATICAL APPROXIMATION<br /><br /></span> </div> <div style="text-align: justify;"><span style="font-family:arial;">Numerical approximation is defined as a figure reoresenta to a number whose exact value is the twelfth to the extent that the figure was closer to the exact value, it will be a better approximation of that number.</span><img src="file:///C:/DOCUME%7E1/equipo1/CONFIG%7E1/Temp/moz-screenshot-8.jpg" alt="" /><br /><br /><br /><br /><br /></div><br /><span style="font-family:arial;"><br /></span><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-weight: bold; color: rgb(204, 51, 204);font-family:arial;" >SIGNIFICANT FIGURES</span><br /></div><span style="font-weight: bold; color: rgb(204, 51, 204);font-family:arial;" ><br /></span></div><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj03UyG3mTb7FFtByqxPLUzFwkX_Sz6eaePyxz_avlEsVLwrtcWshoxYT_Ql7HSp5M2sv4CZf9qwsh2XjieHxtifLE9MRqfBvIYTn-VAMDu0wNS3WgiGUt0ls2BCID6O4D7wjFvMhNFp3XN/s1600/Image1825.jpg"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer; width: 302px; height: 202px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj03UyG3mTb7FFtByqxPLUzFwkX_Sz6eaePyxz_avlEsVLwrtcWshoxYT_Ql7HSp5M2sv4CZf9qwsh2XjieHxtifLE9MRqfBvIYTn-VAMDu0wNS3WgiGUt0ls2BCID6O4D7wjFvMhNFp3XN/s320/Image1825.jpg" alt="" id="BLOGGER_PHOTO_ID_5496051955086506018" border="0" /></a></div><div style="text-align: justify;"><span style="font-family:arial;">The significant figures (or significant digits) represent the use of a level of uncerta</span><span style="font-family:arial;">inty under certain approximations</span> <span style="font-family:arial;">The use of these considers the last digit of approach is</span><span style="font-family:arial;"> uncertain, for example, to determine the volume of a liquid using a graduated cylinder with a precision of 1 m</span><span style="font-family:arial;">l, implies an uncertainty range of 0.5 ml. It may be said that the volume of 6ml of 5.5 ml will be really to 6.5 ml. The previous volume is repr</span><span style="font-family:arial;">esented as (6.0 ± 0.5) ml. For specific values closer would have to use other instruments of greater precision, for example, a specimen finest divisions and t</span><span style="font-family:arial;">hus obtain (6.0 ± 0.1) ml or something more satisfying as the required accuracy.</span> </div><br /><br /><span style="font-family:arial;"><br /></span><div style="text-align: left;"><div style="text-align: center;"><span style="font-weight: bold; color: rgb(204, 102, 204);font-family:arial;" >ACCURACY AND PRECISION</span><br /></div><br /><br /><br /></div><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjD5jzwzRdN1-JkO2vYTXU86F9dOJNNPeVPCTGuecFP5k2Cnj5JpQrIBcJA7HCiocqDAugvCq2sdiDBe_mdyjaxSUBGUUMn-z7adyK6T3l7znAkRtykanhcgiPBgVbJyiTeOWb75aW6W9f_/s1600/precision_exactitud.jpg"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer; width: 313px; height: 269px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjD5jzwzRdN1-JkO2vYTXU86F9dOJNNPeVPCTGuecFP5k2Cnj5JpQrIBcJA7HCiocqDAugvCq2sdiDBe_mdyjaxSUBGUUMn-z7adyK6T3l7znAkRtykanhcgiPBgVbJyiTeOWb75aW6W9f_/s320/precision_exactitud.jpg" alt="" id="BLOGGER_PHOTO_ID_5496053153757403762" border="0" /></a> <div style="text-align: justify;"><span style="font-family:arial;">Accuracy refers to the dispersion of the set of values from repeated me</span><span style="font-family:arial;">asure</span><span style="font-family:arial;">ments of a magnitude. The lower the spread the greater the accuracy. A common measure of variabil</span><span style="font-family:arial;">ity is the standard deviation of measurements and precision can be estimated as a function of it.</span> <span style="font-family:arial;">Accuracy refers to how close the actual value is the measured value. In statistical terms, accuracy is related to the bias of an estimate. The smaller the bias is a more accurate estimate.</span> <span style="font-family:arial;">When we </span><span style="font-family:arial;">express the accura</span><span style="font-family:arial;">cy of a result is expressed by the absolute error is the difference betwee</span><span style="font-family:arial;">n the experimental value and the true value.</span><br /></div><div style="text-align: center;"><br /></div><div style="text-align: center;"><br /><br /><br /><br /></div> <div style="text-align: center;"><span style="color: rgb(153, 51, 153); font-weight: bold;font-family:arial;" >NUMERICAL STABILITY<br /><br /><br /></span></div><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHKVxzWsFSUI7oB6XtXK_GgWobQu13VSKqAXhDZQx8yuI7I7ZrKqgDPobmBzEjTiPPkG0mCTOuuvU0vvt2uzPXc5ZcC4rFyuc8FIbDmJVLQiFUtSs1zOwDmHSY440k9jJ4MDqLhxyu70_T/s1600/VIP1.jpg"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer; width: 320px; height: 266px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHKVxzWsFSUI7oB6XtXK_GgWobQu13VSKqAXhDZQx8yuI7I7ZrKqgDPobmBzEjTiPPkG0mCTOuuvU0vvt2uzPXc5ZcC4rFyuc8FIbDmJVLQiFUtSs1zOwDmHSY440k9jJ4MDqLhxyu70_T/s320/VIP1.jpg" alt="" id="BLOGGER_PHOTO_ID_5496056806658332834" border="0" /></a><div style="text-align: justify;"><span style="font-family:arial;">In the mathematical </span><span style="font-family:arial;">subfield of numerical analysis, numerical stability is a property of numerical algorithms. Describe how errors in the input data are propagated through the algorithm. In a stable method, errors due to approximations are mitigated as appropriate computing. In an unstable method, any error in the processing is magnified as the calculation applicable. Methods unstable quickly generate waste and are useless for numerical processing.</span> <br /></div><br /><span style="font-family:arial;"><br /><br /></span><div style="text-align: center;"><div style="text-align: left;"><br /><span style="font-family:arial;"><span style="font-weight: bold; color: rgb(204, 51, 204);"><br /></span></span><div style="text-align: center;"><span style="font-family:arial;"><span style="font-weight: bold; color: rgb(204, 51, 204);">CONVERGENCE</span></span><br /></div><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCLHD9FHn2TYjAtsT8O_E9BFt3Qf1z7Onr12ZaS-ZaOK69RQZwGSGgR-_uIO5R_m7YuQJbKt0PEC6k6agJJ0NdFATRmZHd1hvSnHfYee2Ec-5ab5Hp6qPFu5zvY3PqBXeYVDhF5ea3QN4I/s1600/convergencia.gif"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer; width: 320px; height: 254px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCLHD9FHn2TYjAtsT8O_E9BFt3Qf1z7Onr12ZaS-ZaOK69RQZwGSGgR-_uIO5R_m7YuQJbKt0PEC6k6agJJ0NdFATRmZHd1hvSnHfYee2Ec-5ab5Hp6qPFu5zvY3PqBXeYVDhF5ea3QN4I/s320/convergencia.gif" alt="" id="BLOGGER_PHOTO_ID_5496054676252509874" border="0" /></a><br /><br /></div><br /></div> <div style="text-align: justify;"><span style="font-family:arial;">In mathematical analysis, the concept of convergence refers to the p</span><span style="font-family:arial;">roperty they own some numerical sequences tend to a limit. This concept is very general and depending on the nature of the set where the sequence is defined, it can take several forms.</span><br /></div><br /><br /><br /><br /><br /><span style="font-style: italic;font-family:arial;" >fuente</span><span style="font-style: italic;font-family:arial;" ><br /></span><ul><li><span style="font-style: italic;font-family:arial;" >George E. Forsythe, Michael A. Malcolm, and Cleve B. Moler. Computer Methods for Mathematical Computations. Englewood Cliffs, NJ: Prentice-Hall, 1977. (See Chapter 5.)</span></li></ul><ul><li><span style="font-style: italic;font-family:arial;" > William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling. NumericalRecipes in C. Cambridge, UK: Cambridge University Press, 1988. (See Chapter 4.)</span></li></ul>MEIBY ALEJANDRA TOLEDO ARIZAhttp://www.blogger.com/profile/03585855169767775681noreply@blogger.com0tag:blogger.com,1999:blog-8109722156768409655.post-23440584797259982982010-05-15T16:15:00.000-07:002010-07-20T16:28:37.203-07:00MATHEMATICAL MODEL<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8EttcznkPnNFx6svWAzqUOltEo65RQp63gqAmZjnmw5_j6Ow1dgPwwZCnDqIaQamHIDDW2lGVU24RZ9xNKc74al_yzvSx9sOqJO_Twuq539YlhDslvKmXGFr05835E7xB3vqwnydhqYSk/s1600/tego.jpg"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 255px; height: 267px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8EttcznkPnNFx6svWAzqUOltEo65RQp63gqAmZjnmw5_j6Ow1dgPwwZCnDqIaQamHIDDW2lGVU24RZ9xNKc74al_yzvSx9sOqJO_Twuq539YlhDslvKmXGFr05835E7xB3vqwnydhqYSk/s320/tego.jpg" alt="" id="BLOGGER_PHOTO_ID_5471651088773715810" border="0" /></a>
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<br />MATHEMATICAL MODEL</span>
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<br /></span></span></div><div style="text-align: justify;"><span id="result_box" class="long_text" style="font-family:arial;"><span style="" title="">A product model is an abstraction of a real system, </span><span style="background-color: rgb(255, 255, 255);" title="">eliminating the complexities and making relevant assumptions, applies </span><span style="background-color: rgb(255, 255, 255);" title="">a mathematical technique and obtained a symbolic representation of it.</span></span>
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<br />A mathematical model comprises at least three basic sets of </span><span style="background-color: rgb(255, 255, 255);" title="">elements:
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<br /></span></span><ul style="font-weight: bold; color: rgb(204, 51, 204);font-family:arial;"><li><span id="result_box" class="medium_text"><span style="" title="">Decision variables and parameters</span></span></li></ul><span id="result_box" class="medium_text" style="font-family:arial;"><span style="" title="">The decision variables are unknowns to be determined </span><span style="background-color: rgb(255, 255, 255);" title="">from the model solution. </span><span style="background-color: rgb(255, 255, 255);" title="">The parameters represent the values </span><span style="background-color: rgb(255, 255, 255);" title="">known to the system or that can be controlled.</span></span>
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<br /><ul style="font-weight: bold; color: rgb(204, 51, 204);font-family:arial;"><li><span id="result_box" class="long_text"><span style="" title="">Restrictions</span></span></li></ul><span id="result_box" class="long_text" style="font-family:arial;"><span style="background-color: rgb(255, 255, 255);" title="">Constraints are relations between decision variables and </span><span style="background-color: rgb(255, 255, 255);" title="">magnitudes that give meaning to the solution of the problem and delimit values </span><span title="">feasible. </span><span style="" title="">For example if one of the decision variables representing the number </span><span style="background-color: rgb(255, 255, 255);" title="">employees of a workshop, it is clear that the value of that variable can not </span><span title="">be negative.
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<br /></span></span><ul style="color: rgb(204, 51, 204); font-weight: bold;font-family:arial;"><li><span id="result_box" class="long_text"><span style="" title="">Objective Function</span></span></li></ul><span id="result_box" class="long_text" style="font-family:arial;"><span style="background-color: rgb(255, 255, 255);" title="">The objective function is a mathematical relationship between variables </span><span style="background-color: rgb(255, 255, 255);" title="">decision parameters and a magnitude representing the target or product </span><span title="">system. </span><span style="background-color: rgb(255, 255, 255);" title="">For example if the objective is to minimize system costs </span><span style="background-color: rgb(255, 255, 255);" title="">operation, the objective function should express the relationship between cost and </span><span title="">decision variables. </span><span style="background-color: rgb(255, 255, 255);" title="">The optimal solution is obtained when the value of cost </span><span style="background-color: rgb(255, 255, 255);" title="">is minimal for a set of feasible values of the variables. </span><span title="">Ie there </span><span style="background-color: rgb(255, 255, 255);" title="">to determine the variables x1, x2, ..., xn that optimize the value of Z = f (x1, </span><span style="background-color: rgb(255, 255, 255);" title="">x2, ..., xn) subject to constraints of the form g (x1, x2, ..., xn) b. </span><span title="">Where x1, x2, </span><span style="background-color: rgb(255, 255, 255);" title="">..., Xn are the decision variables Z is the objective function, f is a function </span><span title="">mathematics.</span></span>
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<br /><div style="text-align: center; font-weight: bold; color: rgb(204, 51, 204);font-family:arial;"><span id="result_box" class="short_text"><span style="" title="">HOW TO DEVELOP A MATEMATICAL MODEL</span></span>
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<br /><span id="result_box" class="long_text" style="font-family:arial;"><span style="" title=""> <span style="color: rgb(204, 51, 204);">1.</span> </span><span style="" title="">Find a real world problem.
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<br /><span style="color: rgb(204, 51, 204);"> </span></span><span title=""><span style="color: rgb(204, 51, 204);">2</span>. </span><span style="background-color: rgb(255, 255, 255);" title="">Formulate a mathematical model of the problem, identifying variables (dependent and independent) and establishing hypotheses simple enough to be treated mathematically.
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<br /><span style="color: rgb(204, 102, 204);"> </span></span><span title=""><span style="color: rgb(204, 102, 204);">3</span>. </span><span style="background-color: rgb(255, 255, 255);" title="">Apply mathematical knowledge that has to reach mathematical conclusions.
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<br /><span style="color: rgb(204, 51, 204);"> </span></span><span style="background-color: rgb(255, 255, 255);" title=""><span style="color: rgb(204, 51, 204);">4</span>. </span><span style="background-color: rgb(255, 255, 255);" title="">Compare the data obtained as predictions with real data. </span><span style="" title="">If the data are different, the process is restarted.</span></span>
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<br /><div style="text-align: center;font-family:arial;"><span style="font-weight: bold; color: rgb(204, 51, 204);" id="result_box" class="short_text"><span style="" title="">CLASSIFICATION OF MODELS</span></span>
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<br /><ul style="font-family:arial;"><li><span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title=""> <span style="color: rgb(204, 51, 204);">Heuristic Models</span></span></span><span id="result_box" class="short_text" style="font-family:arial;"><span style="background-color: rgb(255, 255, 255);" title="">:</span></span><span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title=""> (Greek euriskein 'find, invent'). </span><span style="" title="">Are those that are based on the explanations of natural causes or mechanisms that give rise to the phenomenon studied.</span></span></li></ul><ul style="font-family:arial;"><li><span style="color: rgb(204, 51, 204);" id="result_box" class="long_text"><span style="" title=""> </span><span style="background-color: rgb(255, 255, 255);" title="">Empirical models</span></span><span id="result_box" class="short_text" style="font-family:arial;"><span style="background-color: rgb(255, 255, 255);" title="">:</span></span><span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title=""> (Greek empeirikos on the 'experience'). </span><span style="background-color: rgb(255, 255, 255);" title="">They are using direct observations or the results of experiments studied phenomenon.</span></span></li></ul><span id="result_box" class="long_text" style="font-family:arial;"><span style="background-color: rgb(255, 255, 255);" title="">
<br /></span><span style="background-color: rgb(255, 255, 255);" title="">Mathematical models are also different names in various applications. </span><span style="background-color: rgb(255, 255, 255);" title="">The following are some types to which you can adapt a mathematical model of interest. </span><span style="background-color: rgb(255, 255, 255);" title="">According to its scope models:
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<br /><ul style="font-family:arial;"><li><span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title=""></span><span style="color: rgb(204, 51, 204);" title="">Conceptual models </span><span style="background-color: rgb(255, 255, 255); color: rgb(204, 51, 204);" title=""></span></span><span style="color: rgb(204, 51, 204);font-family:arial;" id="result_box" class="short_text" ><span style="background-color: rgb(255, 255, 255);" title="">:</span></span><span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title="">Are those that reproduce by mathematical formulas and algorithms more or less complex physical processes that occur in nature.</span></span></li></ul><ul style="font-family:arial;"><li><span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title=""></span><span style="background-color: rgb(255, 255, 255);" title=""><span style="color: rgb(204, 51, 204);">Mathematical model of optimization</span> </span><span style="" title=""></span></span><span id="result_box" class="short_text" style="font-family:arial;"><span style="background-color: rgb(255, 255, 255);" title="">:</span></span><span id="result_box" class="long_text"><span style="" title="">Mathematical optimization models are widely used in various branches of engineering to solve problems that are by nature indeterminate, ie have more than one possible solution.</span></span></li></ul>
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<br /><div style="text-align: center;"><span id="result_box" class="short_text"><span style="" title=""><span style="font-weight: bold; color: rgb(204, 51, 204);">CATEGORIES FOR ITS APPLICATION</span></span></span>
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<br /></span></span><div style="text-align: justify;"><span id="result_box" class="long_text"><span style="" title="">For use commonly used in the following three areas, however there are many others such as finance, science and so on.</span></span>
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<br /><span id="result_box" class="long_text"><span style="" title=""></span></span></div><ul style="text-align: justify;"><li><span id="result_box" class="long_text"><span style="" title=""> </span><span title=""> <span style="color: rgb(204, 51, 204);">Simulation</span></span></span><span style="color: rgb(204, 51, 204);font-family:arial;" id="result_box" class="short_text" ><span style="background-color: rgb(255, 255, 255);" title="">:</span></span><span id="result_box" class="long_text"><span title=""> </span><span style="" title="">In situations accurately measurable or random, for example linear programming aspects precisely when, and probabilistic or heuristic when it is random.</span></span></li></ul><ul style="text-align: justify;"><li><span id="result_box" class="long_text"><span style="" title=""> <span style="color: rgb(204, 51, 204);"> </span></span><span style="color: rgb(204, 51, 204);" title="">Optimization </span></span><span id="result_box" class="short_text" style="font-family:arial;"><span style="background-color: rgb(255, 255, 255);" title="">:</span></span><span id="result_box" class="long_text"><span title=""></span><span style="background-color: rgb(255, 255, 255);" title="">To determine the exact point to resolve any administrative problems, production, or other status. </span><span style="background-color: rgb(255, 255, 255);" title="">When the optimization is complete or nonlinear, combination, refers to mathematical models little predictable, but they can fit into any existing alternative and approximate quantification.</span></span></li></ul><ul style="text-align: justify;"><li><span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title=""> </span><span style="color: rgb(204, 51, 204);" title=""> Control</span></span><span style="color: rgb(204, 51, 204);font-family:arial;" id="result_box" class="short_text" ><span style="background-color: rgb(255, 255, 255);" title="">:</span></span><span 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italic;font-family:arial;" id="result_box" class="short_text" ><span style="background-color: rgb(255, 255, 255);" title="">:</span></span><span class="longtext"></span></p> <ul style="font-style: italic; text-align: justify;font-family:arial;"><li>http://www.investigacion-operaciones.com/Formulacion%20Problemas.htm</li></ul><ul face="arial" style="font-style: italic; text-align: justify;"><li><cite style="font-style: normal;" id="CITAREFR.C3.ADos.2C_Sixto1995"><span style="font-variant: small-caps;">Ríos, Sixto</span> (1995). Modelización. Alianza Universidad.</cite></li></ul>MEIBY ALEJANDRA TOLEDO ARIZAhttp://www.blogger.com/profile/03585855169767775681noreply@blogger.com0tag:blogger.com,1999:blog-8109722156768409655.post-82461870761143251292010-05-12T12:28:00.001-07:002010-07-20T16:29:07.971-07:00ROOTS OF EQUATIONS<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpwGB2IK-Aff3Uz4M5WIOJs2GaEHNkT-2ScOcyoeu7wzkmwe8yCugakbNA6cYk5utGNsiMGaGFl-9sjWU28AKVHygYYeC_g8vA_TqNn2F5vo-nZiC_pqTv4rOQD_MotNYySwNFKJx2l6cm/s1600/meiby.jpg"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer; width: 253px; height: 259px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpwGB2IK-Aff3Uz4M5WIOJs2GaEHNkT-2ScOcyoeu7wzkmwe8yCugakbNA6cYk5utGNsiMGaGFl-9sjWU28AKVHygYYeC_g8vA_TqNn2F5vo-nZiC_pqTv4rOQD_MotNYySwNFKJx2l6cm/s320/meiby.jpg" alt="" id="BLOGGER_PHOTO_ID_5471652683449213954" border="0" /></a><br /><br /><br /><div style="text-align: center;font-family:arial;"><span style="color: rgb(255, 102, 102); font-weight: bold;">ROOTS OF EQUATIONS</span><br /></div><br /><div style="text-align: justify;"><span style="font-family:arial;">The purpose of calculating the roots of an equation to determine the values of x for which holds:</span><br /><br /><img style="font-family: arial;" src="file:///C:/DOCUME%7E1/equipo1/CONFIG%7E1/Temp/moz-screenshot-2.jpg" alt="" /><br /></div><div style="font-family: arial; text-align: center;">f (x) = 0 (28) </div><div style="text-align: justify;"><br /><br /><br /><br /><br /></div><div style="text-align: justify;"><div style="text-align: justify;"><span style="font-family:arial;">The determination of the roots of an equation is one of the oldest problems in mathematics and there have been many efforts in this regard. Its impo</span><span style="font-family:arial;">rtance is that if we can determine the roots of an equation we can also determine the maximum and minimum eigenvalues of matrices, solving systems of linear differential equations, etc ...</span><br /><br /><span style="font-family:arial;">The determination of the solutions of equation (28) can</span><span style="font-family:arial;"> be a very difficult problem. If f (x) is a polynomial function of grade 1 or 2, know simple expressions that allow us to determine its roots. For polynomials of degree 3 or 4 is necessary to use complex and laborious methods. However, if f (x) is of degree greater than four is either not polynomial, there is no formula known to help identify the zeros of the equation (except in very special cases).</span><br /><br /><span style="font-family:arial;">In general, the methods for finding the real roots of algebraic equations and transcendental </span><span style="font-family:arial;">methods are divided into intervals and open methods.</span><br /></div><br /><br /></div><ul style="text-align: justify;font-family:arial;"><li><span style="color: rgb(255, 102, 102); font-weight: bold;">INTERVAL METHODS</span>: exploit the fact that typically a function changes sign in the vicinity of a root. They get this name because it needs two initial values to be "encapsulated" to the root. Through such methods will gradually reduce the size of the interval so that the repeated application of the methods always produce increasingly close approximations to the actual value of the root, so methods are said to be convergen.</li></ul><div style="text-align: justify;"><br /><a style="font-family: arial;" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXbR_rWJExrY8hJBz04PIUYLk0AxVGP_oKAEjZUSZHOgNNyBvECnRzKHY1aygvSqdPOUty38B2GLIeplAHdHWnS7brsgseUA8RuNvvK13UKOSBJJynBBS9buZ1vclZUJcT1WcaBIn4cj7S/s1600/image002.gif"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 412px; height: 196px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXbR_rWJExrY8hJBz04PIUYLk0AxVGP_oKAEjZUSZHOgNNyBvECnRzKHY1aygvSqdPOUty38B2GLIeplAHdHWnS7brsgseUA8RuNvvK13UKOSBJJynBBS9buZ1vclZUJcT1WcaBIn4cj7S/s320/image002.gif" alt="" id="BLOGGER_PHOTO_ID_5471612660790863362" border="0" /></a><br /><span style="color: rgb(255, 0, 0);font-family:arial;" id="result_box" class="long_text" ><span style="" title="">In Figure 2.1 is seen as the function changes + f (x) a - f (x), as it passes through the root c. This is because f (c) = 0 and necessarily pass function of positive to negative quadrant </span><span title="">x. </span><span style="background-color: rgb(255, 255, 255);" title="">In some cases, to be seen later this does not happen, for now it will be assumed as shown. </span><span style="background-color: rgb(255, 255, 255);" title="">The methods they use open sign changes in order to place the root (point c), but it must then establish a range (such as [a, b]).</span></span><br /><br /><span style="color: rgb(204, 51, 204);font-family:arial;" id="result_box" class="long_text" ><span style="" title=""><span style="color: rgb(255, 0, 0);">Similarly happens when the function passes through the point e, the change occurs-f (x) + f (x), to find the root of the method requires an interval as [d, f]</span>.</span></span><br /><br /><br /><span id="result_box" class="short_text" style="font-family:arial;"><span style="" title="">The main methods are Interval</span></span><span style="font-family:arial;">:</span><br /><br /><span id="result_box" class="medium_text" style="font-family:arial;"><span title=""><span style="font-weight: bold; color: rgb(255, 102, 102);">a</span>. </span><span style="background-color: rgb(255, 255, 255);" title="">Graphical Method</span></span><br /><br /><span id="result_box" class="medium_text" style="font-family:arial;"><span style="font-size:85%;"><span title=""><span style="font-weight: bold; color: rgb(255, 102, 102);">b</span><span style="color: rgb(255, 102, 102);">.</span> </span><span style="background-color: rgb(255, 255, 255);font-size:100%;" title="" >Bisection Method</span></span></span><br /><br /><span id="result_box" class="medium_text" style="font-family:arial;"><span style="font-size:85%;"><span title="" style="font-size:100%;"><span style="font-weight: bold; color: rgb(255, 102, 102);">c.</span> </span><span style="background-color: rgb(255, 255, 255);font-size:100%;" title="" >Linear Interpolation Method</span></span></span><br /><br /><span id="result_box" class="medium_text" style="font-family:arial;"><span style="font-size:85%;"><span style="background-color: rgb(255, 255, 255);font-size:100%;" title="" ><span style="font-weight: bold; color: rgb(255, 102, 102);">d</span>.</span></span></span><span style=";font-family:arial;font-size:100%;" ><span id="result_box" class="short_text"><span style="" title=""> methods of false position</span></span></span><br /><br /></div><ul style="text-align: justify;font-family:arial;"><li><span style="font-weight: bold; color: rgb(255, 102, 102);">OPEN METHODS:</span> in contrast, are based on formulas that require a single initial value x (initial approach to the root). Sometimes these methods away from the real value of the root grows the number of iterations.<br /></li></ul><div style="text-align: justify;"><br /><span id="result_box" class="short_text" style="font-family:arial;"><span style="" title="">Open the main methods are:</span></span><br /><br /><span id="result_box" class="short_text" style="font-family:arial;"><span title=""><span style="font-weight: bold; color: rgb(255, 102, 102);">a.</span> </span><span title="">Newton Raphson method.</span></span><br /><br /><span id="result_box" class="short_text" style="font-family:arial;"><span style="font-weight: bold; color: rgb(255, 102, 102);" title="">b.</span></span><span id="result_box" class="short_text" style="font-family:arial;"><span style="" title=""> Secant method</span></span><br /><br /><span id="result_box" class="short_text" style="font-family:arial;"><span style="font-weight: bold;" title=""><span style="color: rgb(255, 102, 102);">c</span>.</span></span><span id="result_box" class="short_text" style="font-family:arial;"><span style="" title=""> Multiple roots</span></span><br /><span style="font-family:arial;">.</span><br /><span style="font-family:arial;"><span style="font-style: italic;font-family:arial;" >fuente</span></span><span style="font-style: italic;font-family:arial;" >:</span><!--[if !supportLists]--><br /><span style="font-family:Symbol;">·<span style="font-size:7;"> </span></span><!--[endif]--><span style="font-style: italic;font-family:arial;" class="SpellE" >Burden</span><span style="font-style: italic;font-family:arial;" > Richard L. & </span><span style="font-style: italic;font-family:arial;" class="SpellE" >Faires</span><span style="font-style: italic;font-family:arial;" > J. </span><span style="font-style: italic;font-family:arial;" class="SpellE" >Douglas</span><span style="font-style: italic;font-family:arial;" >, </span><i style="font-family: arial; font-style: italic;">Análisis numérico</i><span style="font-style: italic;font-family:arial;" >. 2ª. </span><span style="font-style: italic;font-family:arial;" class="SpellE" >ed</span><span style="font-style: italic;font-family:arial;" >., México, Grupo Editorial </span><span style="font-style: italic;font-family:arial;" class="SpellE" >Iberoamérica</span><span style="font-style: italic;font-family:arial;" >, 1993.</span><!--[if !supportLists]--><br /><span style="font-style: italic;font-family:Symbol;" lang="EN-US">·<span style="font-size:7;"> </span></span><!--[endif]--><span style="font-style: italic;font-family:arial;" class="SpellE" >Chapra</span><span style="font-style: italic;font-family:arial;" > </span><span style="font-style: italic;font-family:arial;" class="SpellE" >Steven</span><span style="font-style: italic;font-family:arial;" > C. & </span><span style="font-style: italic;font-family:arial;" class="SpellE" >Canale</span><span style="font-style: italic;font-family:arial;" > </span><span style="font-style: italic;font-family:arial;" class="SpellE" >Raymond</span><span style="font-style: italic;font-family:arial;" > P., </span><i style="font-family: arial; font-style: italic;">Métodos numéricos para ingenieros</i><span style="font-style: italic;font-family:arial;" >. </span><span style="font-style: italic;font-family:arial;" lang="EN-US">4ª. ed., México, McGraw-Hill, 2003</span><br /><br /><img style="font-family: arial; font-style: italic;" src="file:///C:/DOCUME%7E1/equipo1/CONFIG%7E1/Temp/moz-screenshot.jpg" alt="" /><img style="font-family: arial; font-style: italic;" src="file:///C:/DOCUME%7E1/equipo1/CONFIG%7E1/Temp/moz-screenshot-1.jpg" alt="" /><br /></div><span style="font-family:arial;"><br /></span>MEIBY ALEJANDRA TOLEDO ARIZAhttp://www.blogger.com/profile/03585855169767775681noreply@blogger.com0