一种求任意埃尔米特广义特征值的方法  

An Algorithm for Hermitian Indefinite Generalized Eigenvalue Problems

作　　者：征道生[1] 徐兰[1] 

机构地区：[1]华东师范大学数学系

出　　处：《华东师范大学学报（自然科学版）》1993年第3期34-43,共10页Journal of East China Normal University(Natural Science)

摘　　要：本文利用五种复变换矩阵(其中四种为作者新提出),给出一种求解埃尔米特广义特征值问题Ax=λBx的方法,这里A,B为n阶任意埃尔米特阵.可说是[1]和[2]中方法的改进与推广,[1]中讨论了A、B实对称B非奇异的情形,[2]中的MDR法只能用于A,B实对称B半正定的情形.它们都不能解决B为奇异且不定的情形,也不能解决A,B为埃尔米特的情形.本文还对[1]中的中断情况作了改进,对MDR方法的改进在别处讨论,新方法称CHR法.In this paper, five complex transformation matrices (four of them are proposed by the authers) and least square method are used, and an algorithm for Hermitian indefinite generalized eigenvalue problem Ax=λBx is established.When A and B are real symmetric and B is nonsingular, HR algorithm can be used to solve it.Here, A and B are Hermitian and B may be singular.The new algorithm is called 'CHR'.Four new complex transformation matrices are: Unitary diagonal exchange matrix T; Complex quasi-Givens matrix; Fast complex quasi-Givena transformation matrix and Complex quasi-House holder matrix.

关 键 词：不定埃米特阵 广义特征值 CHR法 

分 类 号：O151.21[理学—数学]