MATHEMATICAL APPROXIMATION

MATHEMATICAL APPROXIMATION

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.

SIGNIFICANT FIGURES

The significant figures (or significant digits) represent the use of a level of uncertainty under certain approximations The use of these considers the last digit of approach is uncertain, for example, to determine the volume of a liquid using a graduated cylinder with a precision of 1 ml, 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 represented 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 thus obtain (6.0 ± 0.1) ml or something more satisfying as the required accuracy.

ACCURACY AND PRECISION

Accuracy refers to the dispersion of the set of values from repeated measurements of a magnitude. The lower the spread the greater the accuracy. A common measure of variability is the standard deviation of measurements and precision can be estimated as a function of it. 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. When we express the accuracy of a result is expressed by the absolute error is the difference between the experimental value and the true value.

NUMERICAL STABILITY

In the mathematical 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.

CONVERGENCE

In mathematical analysis, the concept of convergence refers to the property 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.

fuente

• George E. Forsythe, Michael A. Malcolm, and Cleve B. Moler. Computer Methods for Mathematical Computations. Englewood Cliffs, NJ: Prentice-Hall, 1977. (See Chapter 5.)

• William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling. NumericalRecipes in C. Cambridge, UK: Cambridge University Press, 1988. (See Chapter 4.)