求解对称带状广义特征值问题的扩展分治算法  

An Extended Divide and Conquer Algorithm for Solving Real Symmetric Band Generalized Eigenvalue Problem

作　　者：魏立峰[1] 李晓梅[2] 

机构地区：[1]国防科技大学计算机学院,长沙410073 [2]装备指挥技术学院,北京101416

出　　处：《计算机研究与发展》2004年第5期861-867,共7页Journal of Computer Research and Development

基　　金："十五"国防预研基金项目

摘　　要：提出了分布式环境下计算对称带状广义特征值问题的一种扩展分治算法 ,给出了特征值分割定理及其证明 算法在扩展分治的基础上 ,利用二分压缩结合广义Rayleigh商迭代计算广义特征对 理论分析和数值实验表明 ,对于窄带宽大规模的广义特征值问题 ,该分治算法明显优于LAPACK软件包 结合并行性好的多分法 。In this paper, an extended divide and conquer algorithm is intended proposed, which is for solving the real symmetric band generalized eigenvalue problem under distributing environment Eigenvalue partition theorem is presented and proved Based on divide and conquer by extension, this algorithm computes generalized eigenpaires of symmetric band matrix pencil by bisection and generalized Rayleigh quotient iteration Theoretic analysis and numerical results show that this algorithm is better than the classic software package LAPACK when bandwidth is small and the scale is large Combined with multisection, which has good parallelism, it got good effects under distributed environments

关 键 词：扩展分治 对称带状 广义特征值问题 惯性 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]