Jacobi迭代法

迭代公式

代码

import numpy as np

def Jacobi(A,b,n=1000,eps=1e-6):
    if len(A) == len(b):
        x = []
        for i in range(len(A)):
            x.append(0)
        count = 0
        while count < n:
            nx = []
            for i in range(len(x)):
                nxi = b[i]
                for j in range(len(A[i])):
                    if j!=i:
                        nxi -= A[i][j]*x[j]
                nxi = nxi/A[i][i]
                nx.append(nxi)
            if np.linalg.norm(np.mat(nx)-np.mat(x)) < eps:
                return nx
            x = nx
            count = count + 1
        return False
    else:
        return False

A = [[8,-3,2],[4,11,-1],[6,3,12]]
b = [20,33,36]
print(Jacobi(A,b,1000,1e-10))

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Gauss-Seidel迭代法

迭代公式

代码

import numpy as np

def Gauss_Seidel(A,b,n=1000,eps=1e-6):
    if len(A) == len(b):
        x = []
        for i in range(len(A)):
            x.append(0)
        count = 0
        while count < n:
            nx = []
            for i in range(len(x)):
                nxi = b[i]
                for j in range(len(A[i])):
                    if j < i:
                        nxi -= A[i][j]*nx[j]
                    if j > i:
                        nxi -= A[i][j]*x[j]
                nxi = nxi/A[i][i]
                nx.append(nxi) 
            if np.linalg.norm(np.mat(nx)-np.mat(x)) < eps:
                print(count)
                return nx 
            x = nx
            count = count + 1
        return False 
    else:
        return False

A = [[8,-3,2],[4,11,-1],[6,3,12]]
b = [20,33,36]
print(Gauss_Seidel(A,b,1000,1e-10))

SOR

迭代公式

其中.

代码

import numpy as np

def SOR(A,b,w=0.5,n=1000,eps=1e-6):
    if len(A) == len(b):
        x = []
        for i in range(len(A)):
            x.append(0)
        count = 0
        while count < n:
            nx = []
            for i in range(len(x)):
                nxi = b[i]
                for j in range(len(A[i])):
                    if j < i:
                        nxi -= A[i][j]*nx[j]
                    if j > i:
                        nxi -= A[i][j]*x[j]
                nxi = w*nxi/A[i][i]
                nxi += (1-w)*x[i]
                nx.append(nxi) 
            if np.linalg.norm(np.mat(nx)-np.mat(x)) < eps:
                print(count)
                return nx 
            x = nx
            count = count + 1
        return False 
    else:
        return False

A = [[8,-3,2],[4,11,-1],[6,3,12]]
b = [20,33,36]
print(SOR(A,b,0.5,1000,1e-10))