双倍维Jacobi矩阵逆问题的改进算法

THE IMPROVED ALGORITHM ON THE DOUBLE DIMENSIONAL JACOBI MATRIX INVERSE EIGENVALUE PROBLEM

本文给出了一种解决双倍维Jacobi矩阵逆问题的改进算法.该算法避免了重新构造顺序主子矩阵Jn,也避免了计算尾主子矩阵Jn+1,2n的特征多项式以及特征值,因此本文的改进算法具有更好的稳定性和精度.给出的两个数值实例说明,本文的改进算法是有效的,比现有的几种算法具有更高的精度.

This paper proposes an improved algorithm to solve the double dimensional Jacobi matrix inverse eigenvalue problem.The algorithm neither reconstructs the leading principal submatrix Jn nor computes characteristic polynomial of the tail leading principal submatrix Jn+1,2 n and its eigenvalues.Because of them,this algorithm,has the better stability and accuracy.The two given numerical examples illustrate that this improved algorithm is effective and it has higher accuracy than several current algorithms.