非对称广义特征值问题并行处理的一些进展

Some progress of the parallel processing for nonsymmetric generalized eigenvalue problem

广义特征值问题AX =λBX(A、B是N阶方矩阵 )的并行处理是大规模科学与工程计算中的基础问题之一。迄今为止 ,国内外学者对该问题的研究多集中于对称矩阵广义特征值问题的并行处理 ,并形成多种算法和相应软件。而非对称矩阵广义特征值问题并行处理的研究相对进行得较少。介绍作者等人近几年来在非对称广义特征值问题并行处理方面的一些工作。它包括 :QZ算法的并行化 ,并行拟 Eberlein算法及并行同伦数值方法等。

Parallel processing for generalized eigenvalve problem is one of the fundalmental problems in computation science and engineering. The study of this problem has received considerable attention. So far there are very much study of parallel processing for symmetric matrix generalized eigenvalue problem and there are very little study of parallel processing for nonsymmetric matrix generalized eigenvalue problem. In this paper we introduce mainly our work on parallel processing for nonsymmetric matrix generalized eigenvalue problem. It includes parallel QZ algorithm, parallel Eberlein like algorithm and parallel homotopy numerical method.