ROOTS OF EQUATIONS

OPEN METHODS

  
FIXED POINT

  • You want to approximate a root of the equation x3 - 30x2 + 2400 = 0, which we know is in the interval (10,15) through the fixed point method. Which of the following functions would you use to able to expect convergence in the iteration process? Explain your answer.




FIXED POINT METHOD
iteraciones xi h(x) g(x) %error Aprox  %Error Real Et
1 10 10,9544512 410
2 10,9544512 11,2255822 125,488589 2,415296153 1,021006884
3 11,2255822 11,3063489 45,3918085 0,714347846 0,308865411
4 11,3063489 11,3307473 21,6310356 0,215329475 0,093737781





















































  • NEWTON RAPHSON








FX
















I xi xi+1 f'(xi) f(xi) %E Total
1 1 0,319520937 -1,270670566 -0,864664717
2 0,319520937 0,420842873 -2,055595758 0,208276942 1,28075131
3 0,420842873 0,426289001 -1,861966764 0,010140509 0,00322542
4 0,426289001 0,426302751 -1,852628949 2,54736E-05 1,8801E-08
5 0,426302751 0,426302751 -1,852605502 1,61198E-10 1,6098E-09
6 0,426302751 0,426302751 -1,852605502 0 1,6098E-09
7 0,426302751 0,426302751 -1,852605502 0 1,6098E-09
8 0,426302751 0,426302751 -1,852605502 0 1,6098E-09
9 0,426302751 0,426302751 -1,852605502 0 1,6098E-09
10 0,426302751 0,426302751 -1,852605502 0 1,6098E-09
11 0,426302751 0,426302751 -1,852605502 0 1,6098E-09
12 0,426302751 0,426302751 -1,852605502 0 1,6098E-09
13 0,426302751 0,426302751 -1,852605502 0 1,6098E-09
14 0,426302751 0,426302751 -1,852605502 0 1,6098E-09
15 0,426302751 0,426302751 -1,852605502 0 1,6098E-09
16 0,426302751 0,426302751 -1,852605502 0 1,6098E-09
0,426302751 0,426302751 -1,852605502 0 1,6098E-09









































































































































































































































































































































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