双对称非负定阵一类逆特征值问题的最小二乘解  

LEAST-SQUARES SOLUTION OF A CLASS OF INVERSE EIGENVALUE PROBLEMS FOR BISYMMETRIC NONNEGATIVE DEFINITE MATRICES

作　　者：廖安平[1] 谢冬秀[2] 

机构地区：[1]湖南师范大学理学院,长沙410081 [2]大连理工大学应用数学系

出　　处：《计算数学》2001年第2期209-218,共10页Mathematica Numerica Sinica

基　　金：国家自然科学基金资助项目

摘　　要：In this paper, we consider the following two problems: Problem i. Given X ∈ Rmxn,A = diag（λ1,…, λm） > 0, find A E BSR such that where ||AX-X∧||=min, is Frobenius norm, BSR: is the set of all n x n bisymmetric nonnegative definite matrices. Problem Ⅱ. Given A* ∈ Rnxn, find ALS ∈ SE such that||A*-ALS||=inf||A*-A|| where SE is the solution set of problem Ｉ. The existence of the solution for problem Ⅰ, Ⅱ and the uniqueness of the solution for Problem Ⅱ are proved. The general form of SE is given and the expression of ALS is presented.In this paper, we consider the following two problems: Problem i. Given X ∈ Rmxn,A = diag(λ1,…, λm) > 0, find A E BSR such that where ||AX-X∧||=min, is Frobenius norm, BSR: is the set of all n x n bisymmetric nonnegative definite matrices. Problem Ⅱ. Given A* ∈ Rnxn, find ALS ∈ SE such that||A~*-A_(LS)||=inf||A~*-A|| where SE is the solution set of problem Ｉ. The existence of the solution for problem Ⅰ, Ⅱ and the uniqueness of the solution for Problem Ⅱ are proved. The general form of SE is given and the expression of ALS is presented.

关 键 词：双对称非负定阵 逆特征值问题 最小二乘解 FROBENIUS范数 

分 类 号：O241.6[理学—计算数学]