一类特殊类型子空间上Ritz对的性质及其应用  

ON THE RITZ PAIRS WITH RESPECT TO A KIND OF SPECIAL SUBSPACES WITH AN APPLICATION

作　　者：贾仲孝[1] 牛大田[2] 

机构地区：[1]清华大学数学科学系,100084 [2]大连理工大学应用数学系,116024

出　　处：《数值计算与计算机应用》2003年第4期257-261,共5页Journal on Numerical Methods and Computer Applications

基　　金：国家重点基础研究专项基金(G19990328)

摘　　要：§1.引言 设A∈RM×N,定义增广矩阵 (A~)=(O A AT O),(1) 其中上标T表示转置.不失一般性,假设M≥N,设σi,i=1,2,…,N是A的奇异值,ui和ui分别是对应的左右奇异向量,奇异值按从小到大或从大到小的顺序排列,则A的特征值恰好为±σi,i=1,2,…,N和M-N个零,±σi对应的特征向量分别为1/√2(uT i,vT i)T和1/√2(uT i,-vT i)T.We study some properties of the Ritz pairs of an argumented matrix with respect to a kind of special subspaces. It is proved that the projected eigenproblem can be reduced to a half dimensional singular value problem. As an important application, this equivalence allows one to compute a partial SVD of a large scale matrix and refined shifts for use within an implicitly restarted refined bidiagonal-ization Lanczos algorithm (IRRBL), so that the computational cost and the storage requirement can be saved significantly.

关 键 词：Ritz对 增广矩阵 标准正交基 特征值 奇异值 

分 类 号：O151.2[理学—数学]