满秩仿Hermite多项式矩阵的J-谱分解计算

基于仿等价变换实现了满秩仿Hermite多项式矩阵的J-谱分解计算.对于一个满秩的 仿Hermite多项式矩阵,首先用仿等价变换将其变换为单模的满秩仿Hermite多项式矩阵,进 一步再用仿等价变换将其变换为常数满秩矩阵,最后变换为J-矩阵.将这些变换矩阵积累起 来,得到满秩仿Hermite多项式矩阵的J-谱分解.在作者发展的多项式矩阵运算程序库的基础 上,给出了实现所提出的计算方法的算法.数例表明,该方法是有效的.

The Calculation of J-Spectrum Factorization for the Full Rank Para-Hermite Polynomial Matrix

Using the para equivalent transform, we propose a method for calculating the J spectrum factorization for the full rank para Hermite polynomial matrix. For a full rank para Hermite polynomial matrix, we transform it into a uni module full rank para Hermite polynomial matrix by para equivalent transform at first, then into a full rank constant symmetric matrix, and into a J -matrix at last. Accumulating these transforms, we obtain the J -spectrum factorization. Based on the programming package for polynomial matrix developed by the authors, an algorithm which realizes the proposed method is given. The numerical example indicates this method is useful.