Computer simulation of QR algorithm and its application in the matrix eigenvalue problem

The algorithm is a new approach for solving eigenvalue problem which is based on the P (p, q, w) rotation transform; it is the effective way for solving all the eigenvalues and eigenvectors of the general matrix at present, and it is applicable to both cases of the symmetric matrix and non-symmetric matrix. The method uses Householder matrix, first matrix A is transformed into a symmetric tridiagonal matrix, and then use computer simulation for QR algorithm to achieve the eigenvalues of symmetric triangular matrix. QR Algorithm is one of the most effective ways for solving all the eigenvalues and eigenvectors of the small and medium sized matrix at present, and it has good stability and rapid convergence speed.