例題 EX2-8 定點回路法 求非線性方程式 f(x)=exp(x) - 3x^2 = 0

'''
 定點回路法
/* ex2-8.py is used for solving nonlinear equation
 * based on Fixed-Point Algorithm g(x)=x with initial
 * approximation P0.
 */

 例題 EX2-8 定點回路法 求非線性方程式 f(x)=math.exp(x) - 3x^2 = 0
    y= x
    y= (esp(x)/3) ^ 0.5

    與
    y= x
    y= - (esp(x)/3) ^ 0.5

'''
import math
MAX=50
TOL=0.001

def g(x):
    temp=( pow ( ( math.exp(x)/3) ,0.5)+0.0)
    return temp

def g1(x):
    temp=-(pow ( ( math.exp(x)/3) ,0.5)+0.0)
    return temp

i=1
# f(0)= 0.5575 ,
# f(0)=-0.5575 
x0=0.0
print("==============================")
print('x\t\t     x0')
while(i<=MAX):
    x=g(x0)
    print("{%-2d}\t\t {%10.7f}" %(i-1,x0))
    if(abs(x-x0) < TOL):
        print("The Root={%10.7f}  x-x0={%10.7f}\n" %(x,abs(x-x0)))
        break
    i=i+1
    x0=x

print("Fixed-point failed after {%d} iteration.\n"%(i))


i=1
# f(0)= 0.5575 ,
# f(0)=-0.5575 
x0=0.0
print("==============================")
print('x\t\t     x0')
while(i<=MAX):
    x=g1(x0)
    print("{%-2d}\t\t {%10.7f}" %(i-1,x0))
    if(abs(x-x0) < TOL):
        print("The Root={%10.7f}  x-x0={%10.7f}\n" %(x,abs(x-x0)))
        break
    i=i+1
    x0=x

print("Fixed-point failed after {%d} iteration.\n"%(i))

========= RESTART: F:/2018-09勤益科大數值分析/數值分析/PYTHON/ex2-8.py ============
==============================
x      x0
{0 } { 0.0000000}
{1 } { 0.5773503}
{2 } { 0.7705652}
{3 } { 0.8487220}
{4 } { 0.8825453}
{5 } { 0.8975975}
{6 } { 0.9043784}
{7 } { 0.9074499}
{8 } { 0.9088446}
The Root={ 0.9094786}  x-x0={ 0.0006340}

Fixed-point failed after {9} iteration.

==============================
x      x0
{0 } { 0.0000000}
{1 } {-0.5773503}
{2 } {-0.4325829}
{3 } {-0.4650559}
{4 } {-0.4575660}
{5 } {-0.4592828}
The Root={-0.4588887}  x-x0={ 0.0003941}

Fixed-point failed after {6} iteration.

>>>