一种可以解决伴随矩阵中退化本征值数值精度问题的方法是利用位移策略，使退化本征值与其他本征值分开计算。具体实现方法是通过使用QR分解和Wilkinson位移，将伴随矩阵的计算转化为非退化本征值计算。以下是Python代码示例：

import numpy as np 

def compeig(A):
    n = A.shape[0]
    Q = np.eye(n)
    for k in range(n-1):
        x = A[k:,k]
        e1 = np.zeros_like(x)
        e1[0] = 1
        u = np.sign(x[0])*np.linalg.norm(x)*e1 + x
        u = u/np.linalg.norm(u)
        A[k:,k:] = A[k:,k:] - 2*np.outer(u,np.dot(u.T,A[k:,k:]))
        Q[k:,:] = Q[k:,:] - 2*np.outer(u,np.dot(u.T,Q[k:,:]))
    eigvals = []
    while n > 1:
        if abs(A[n-1,n-2]) < 1e-10:
            eigvals.append(A[n-1,n-1])
            A = A[:n-1,:n-1]
            Q = Q[:n-1,:]
            n -= 1
        else:
            mu = A[n-1,n-1]
            A = A - mu*np.eye(n)
            q, r = np.linalg.qr(A)
            Q = Q.dot(q)
            A = r.dot(q) + mu*np.eye(n)
            eigvals.append(mu)
    eigvals.append(A[0,0])
    eigvals.reverse()
    Q = Q.T
    return eigvals, Q

# Example usage:
A = np.array([[0,1,0,0],
              [0,0,1,0],
              [0,0,0,1],
              [1,0,0,1]])

eig