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< 01 | 02 | Newton-Raphson >

Atividade #1.3.02

A função \(f_{1}(x)=x^2+x-6\) tem os raízes: 2 e -3. Para quais pontos iniciais: \([-5.0,-4.0,-1.0,1.0,3.0,5.0]\) o algoritmo ponto fixo converge usando a função iterativa \(\varphi_1,\) respectivamente \(\varphi_2\) ? Em quantas iterações?

Python Listing: ../../Run.Fixed_Point2.py.

from Fixed_Point import *
from Functions2 import *

phis=[phi1,phi2]
x0s=[-5.0,-4.0,-1.0,1.0,3.0,5.0]

n=1
for phi in phis:
    for x0 in x0s:
        xs=Fixed_Point(f1,phi,x0,1.0E-6)
        #print f
        print "phi"+str(n)+": "+str(x0),len(xs),xs[ len(xs)-1 ]
    n+=1

phi1: -5.0 14 2.00000008479
phi1: -4.0 14 2.00000007407
phi1: -1.0 13 1.99999984059
phi1: 1.0 13 1.99999994303
phi1: 3.0 13 2.00000006306
phi1: 5.0 14 1.99999994303
phi2: -5.0 39 -3.00000029069
phi2: -4.0 37 -3.00000038153
phi2: -1.0 41 -2.99999969854
phi2: 1.0 45 -2.99999964272
phi2: 3.0 46 -2.99999964272
phi2: 5.0 44 -2.99999964272

Output from: /usr/bin/python ../../Run.Fixed_Point2.py

< 01 | 02 | Newton-Raphson >