非线性方程的二分法和(线性)插值法python实例

 1 import math
 2 import numpy as np
 3 import matplotlib.pyplot as plt
 4 
 5 a=0.3
 6 b=0.4
 7 h=b-a
 8 p=1e-4
 9 x = np.arange(-0.3, 0.4, 0.0001)#可以自动生成x轴坐标，最小间隔为0.0001
10 y=x**4-3*x+1
11 plt.style.use(‘ggplot‘)#使用‘ggplot风格美化图表’
12 plt.xlabel(u"x")
13 plt.title(u‘Dichotomy for roots‘)
14 plt.plot(x,y,‘r‘,linewidth=2)
15 #计算迭代次数N
16 N=math.ceil((math.log((b-a)/p)/math.log(2)))#向上取整
17 A=[0]*(N+1)
18 B=[0]*(N+1)
19 X=[0]*(N+1)#保存中点
20 F=[0]*(N+1)#保存中点的函数值
21 FA=[0]*(N+1)
22 x1=[0]*(N+1)
23 A[0]=a
24 B[0]=b
25 for i in range(N): 
26     X[i]=(A[i]+B[i])/2
27     F[i]=X[i]**4-3*X[i]+1
28     FA[i]=A[i]**4-3*A[i]+1
29     if F[i]==0:
30        x1=X[i]
31     elif F[i]*FA[i]>0:
32         A[i+1]=X[i]
33         B[i+1]=B[i]
34     elif F[i]*FA[i]<0:
35         A[i+1]=A[i]
36         B[i+1]=X[i]
37     #print(A[i],B[i],F[i],FA[i])
38 print(‘使用二分法迭代%d次后的根为%f‘%(N,X[-2]))
39 print(‘近似解序列为：‘,X[:-1])    

 1 import numpy as np
 2 import matplotlib.pyplot as plt
 3 
 4 a=0.3
 5 b=0.4
 6 x=[0]*1000
 7 X=[]
 8 x1 = np.arange(-0.3, 0.4, 0.0001)#可以自动生成x轴坐标，最小间隔为0.0001
 9 y=x1**4-3*x1+1
10 plt.style.use(‘ggplot‘)#使用‘ggplot风格美化图表’
11 plt.xlabel(u"x")
12 plt.title(u‘Finding the roots by secant‘)
13 plt.plot(x1,y,‘r‘,linewidth=2)
14 
15 def fx(x):
16     y=x**4-3*x+1
17     return y
18 x[0]=a
19 x[1]=b
20 for i in range(1000):
21    root=x[i+1]-(x[i+1]-x[i])/(fx(x[i+1])-fx(x[i]))*fx(x[i+1])
22    x[i+2]=root
23    X.append(root)
24    #if (x[i+2]-x[i+1])<0.0001:计算一次即可
25    if x[i+2]==x[i+1]:
26        break
27    
28 print(‘共迭代%d次‘%i)
29 print(‘正割法求根的近似解序列为：‘,X)
30 print(‘正割法所求根为：‘,X[-1])