谱约束下实对称矩阵束的最隹逼近  

OPTIMAL APPROXIMATION OF REAL SYMMETRIC MATRIX PENCIL UNDER SPECTRAL RESTRICTION

作　　者：戴华[1] 

机构地区：[1]南京大学

出　　处：《高等学校计算数学学报》1990年第2期177-187,共11页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金

摘　　要：§1 引言 用R^(nxm)表示所有nxm实矩阵的全体,R_r^(nxm)表示R^(nxm)中矩阵秩为r的子集,SR^(nxn)表示所有nxn实对称矩阵的全体。OR^(nxn)表示所有nxn正交矩阵的集合。I_n表示n阶单位矩阵。A^T表示矩阵A的转置。||·||_F表示矩阵的Frobenius范数。 本文我们研究如下问题:In this paper,the following problems are discussed.Problem I.given a real n x m matrix X and a real m x m diagonal matrix A.(a).find two real nx asymmetric matrices A and B such that AX= BX.(b).find two real nx n symmetric matrices A and B such that AX=BX and XTBX=Im.Problem II.given two real nx n symmetric matrices A and B,find two real nxn symmetric matrices A and B such thatwhere SAB is the set of solution to Problem I.The general symmetric solutions A and B to Problem I arc derived by using the orthogonal triangular decomposition.The existence and uniqueness of solution to Problem II are considered.Numerical algorithm to compute A and B is suggested.Two numerical examples arc given.

关 键 词：谱约束 实对称矩阵束 最佳逼近 

分 类 号：O241.6[理学—计算数学]