SmtC: Show me the Code
Ole Peter Smith
Instituto de Matemática e Estatística
Universidade Federal de Goiás
http://www.olesmith.com.br

Atividades #1.3
O aspecto mais triste da humanidade hoje
É que ela cresce mais em ciência do que em sabedoria.
Isaac Asimov
< Implementação | 01 | 02 >

Atividade #1.3.01:

Crie um arquivo, Functions2.py, implementando as seguintes funções:
  1. \(f_{1}(x)=x^2+x-6, \quad \varphi_1(x)= \sqrt{6-x}, \quad x_0=1.5;\)
  2. \(f_{2}(x)=x^2+x-6, \quad \varphi_2(x)= \frac{6}{x}-1, \quad x_0=-2.5;\)
  3. \(f_{2}(x)=x^3-9x+3, \quad \varphi_2(x)= \frac{1}{9} x^3+\frac{1}{3}, \quad x_0=0.5;\)
Crie um executavel, Run.Fixed_Point.py, executando o algoritmo Pointo Fixo, conforme indicado acima.
Python Listing: ../../Run.Fixed_Point.py. 
from Fixed_Point import *
from Functions import *
from Functions2 import *

fs=[f1,f2,f3]
phis=[phi1,phi2,phi3]
x0s=[1.5,-2.5,0.5]

n=0
for f in fs:
    phi=phis[n]
    
    xs=Fixed_Point(f,phi,x0s[n],1.0E-6)
    #print f
    print "f"+str(n+1)+" phi"+str(n+1)
    Print(f,xs)
    n+=1

f1 phi1
N    x_k    |f(x_k)|
01    1.500000    2.250000e+00
02    2.121320    6.213203e-01
03    1.969436    1.518840e-01
04    2.007626    3.818998e-02
05    1.998092    9.533865e-03
06    2.000477    2.384319e-03
07    1.999881    5.960265e-04
08    2.000030    1.490100e-04
09    1.999993    3.725228e-05
10    2.000002    9.313083e-06
11    2.000000    2.328270e-06
12    2.000000    5.820675e-07
f2 phi2
N    x_k    |f(x_k)|
01    -2.500000    2.250000e+00
02    -3.400000    2.160000e+00
03    -2.764706    1.121107e+00
04    -3.170213    8.800362e-01
05    -2.892617    5.253817e-01
06    -3.074246    3.767422e-01
07    -2.951698    2.391764e-01
08    -3.032728    1.647121e-01
09    -2.978417    1.074509e-01
10    -3.014493    7.267587e-02
11    -2.990384    4.798582e-02
12    -3.006431    3.219661e-02
13    -2.995722    2.137267e-02
14    -3.002856    1.428918e-02
15    -2.998098    9.508004e-03
16    -3.001269    6.346716e-03
17    -2.999154    4.227566e-03
18    -3.000564    2.819967e-03
19    -2.999624    1.879272e-03
20    -3.000251    1.253162e-03
21    -2.999833    8.353016e-04
22    -3.000111    5.569297e-04
23    -2.999926    3.712589e-04
24    -3.000050    2.475182e-04
25    -2.999967    1.650067e-04
26    -3.000022    1.100069e-04
27    -2.999985    7.333684e-05
28    -3.000010    4.889171e-05
29    -2.999993    3.259426e-05
30    -3.000004    2.172960e-05
31    -2.999997    1.448636e-05
32    -3.000002    9.657591e-06
33    -2.999999    6.438386e-06
34    -3.000001    4.292261e-06
35    -2.999999    2.861506e-06
36    -3.000000    1.907671e-06
f3 phi3
N    x_k    |f(x_k)|
01    0.500000    1.375000e+00
02    0.347222    8.313775e-02
03    0.337985    3.253021e-03
04    0.337623    1.237357e-04
05    0.337609    4.701331e-06
06    0.337609    1.786192e-07
Output from: /usr/bin/python ../../Run.Fixed_Point.py
< Implementação | 01 | 02 >
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