雅可比迭代python 雅可比迭代法程序

线性方程組的求解

雅可比迭代法的公式如下：

　　

 

def Jacobi(a, u):     #u为精度
    n = len(a)        #行数
    n1 = len(a[0])    #列数
    count = 0         #迭代次数
    
    x_k = [0 for i in range(n)]    #第k次迭代后的x的值
    x_k1 = [0 for i in range(n)]   #第k+1次迭代后的x的值
    
    while(1):
        for i in range(n):
            atmp = 0
            for j in range(i):
                atmp += a[i][j] * x_k[j]
            btmp = 0
            for k in range(i+1, n):
                btmp += a[i][k] * x_k[k]
        
            x_k1[i] = (a[i][n1-1] - atmp -btmp) / a[i][i]
        
        #迭代结束条件  1-范数作为结束条件
        if max(x_k1) - max(x_k) < u:
            break
        else:
            count += 1
            for i in range(n):
                x_k[i] = x_k1[i]
    
    return x_k1, count


if __name__ == "__main__":
    paremeters=[[10,-1,-2,7.2], [-1,10,-2,8.3], [-1,-1,5,4.2]]

    print(Jacobi(paremeters,0.000005))