[Python知识库]【数值分析实验】矩阵特征值及特征向量计算：幂法、反幂法、幂法加速（python）

矩阵特征值及特征向量计算

调包

import numpy as np

幂法

#幂法算法 
def M(A,u0,epsilon = 1e-6,M=100):
    uk = u0
    mk_1 = 1
    k = 0
    while True:
        k += 1
        vk = A*uk  
        mk = vk[np.argmax(np.abs(vk))]    
        uk = vk / mk
        if np.abs(mk - mk_1) < epsilon:
            return mk,uk,k
        if k == M:
            print("算法失败！")
            return
        mk_1 = mk

幂法加速

#幂法加速
def M_plus(A,u0,epsilon,M=100,alpha = 0.5):
    uk = u0
    mk_1 = 1
    k = 0
    A = A - alpha * np.eye(len(A))
    while True:
        k += 1
        vk = A*uk  
        mk = vk[np.argmax(np.abs(vk))]    
        uk = vk / mk
        if np.abs(mk - mk_1) < epsilon:
            return mk,uk,k
        if k == M:
            print("算法失败！")
            return
        mk_1 = mk

反幂法

#反幂法
def M_anti(A,u0,epsilon = 1e-6,M=100):
    uk = u0
    mk_1 = 1
    k = 0
    while True:
        k += 1
        vk = np.matrix(np.linalg.inv(A.A))*uk  
        mk = vk[np.argmax(np.abs(vk))]    
        uk = vk / mk
        if np.abs(mk - mk_1) < epsilon:
            return (1/mk).A,uk.A,k
        if k == M:
            print("算法失败！")
            return
        mk_1 = mk