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| COMPUTING THE NEAREST BISYMMETRIC POSITIVE SEMIDEFINITE MATRIX UNDER THE SPECTRAL RESTRICTION | |
| 作者姓名： | 谢冬秀 盛炎平 张忠志 |
| 作者单位： | Department of Basic Science，Beijing Institute of Machinery Industry，Dapartment of Basic Science，Beijing Institute of Machinery Industry，Department of Applied Mathematics，Hunan University Beijing PRC.100085，Beijing PRC.100085，Changsha PRC.410082 |
| 基金项目： | Suported by National Nature Science Foundation of China |
| 摘 要： | Let A and C denote real n × n matrices. Given real n-vectors x1, ... ,xm, m ≤ n, and a set of numbers L = {λ1,λ2,... ,λm}. We describe (I) the set (?) of all real n × n bisymmetric positive seidefinite matrices A such that Axi is the "best" approximate to λixi, i = 1,2,...,m in Frobenius norm and (II) the Y in set (?) which minimize Frobenius norm of ||C - Y||.An existence theorem of the solutions for Problem I and Problem II is given and the general expression of solutions for Problem I is derived. Some sufficient conditions under which Problem I and Problem II have an explicit solution is provided. A numerical algorithm of the solution for Problem II has been presented. |
COMPUTING THE NEAREST BISYMMETRIC POSITIVE SEMIDEFINITE MATRIX UNDER THE SPECTRAL RESTRICTION |
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| Xie Dongxiu.COMPUTING THE NEAREST BISYMMETRIC POSITIVE SEMIDEFINITE MATRIX UNDER THE SPECTRAL RESTRICTION[J].Numerical Mathematics A Journal of Chinese Universities English Series,2003,12(1). | |
| Authors: | Xie Dongxiu |
| Institution: | 1. Department of Basic Science, Beijing Institute of Machinery Industry, Beijing 100085, PRC 2. Department of Basic Science, Beijing Institute of Machinery Industry,Beijing 100085, PRC 3. Department of Applied Mathematics,Hunan University, Changsha 410082,PRC |
| Abstract: | Let A and C denote real n × n matrices. Given real n-vectors x1,……… ,xm,m≤n,and a set of numbers (L)={λ1,λ2…λm}，We descrbe(Ⅰ)the set( ) of all real n × n bisymmetric positive seidefinite matrices A such that Axi is the "best"approximate to λixi, i = 1, 2,..., m in Frobenius norm and (Ⅱ) the Y in set ( )which minimize Frobenius norm of ||C - Y||. An existence theorem of the solutions for Problem Ⅰ and Problem Ⅱ is given andthe general expression of solutions for Problem Ⅰ is derived. Some sufficient conditionsunder which Problem Ⅰ and Problem Ⅱ have an explicit solution is provided. A numer-ical algorithm of the solution for Problem Ⅱ has been presented. |
| Keywords: | bisymmetric positive semidefinite matrices eigenvalues matrix norms |
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