THE PROJECTED GRADIENT-METHOD FOR LEAST-SQUARES MATRIX APPROXIMATIONS WITH SPECTRAL CONSTRAINTS

被引:101
作者
CHU, MT [1 ]
DRIESSEL, KR [1 ]
机构
[1] IDAHO STATE UNIV,DEPT MATH,POCATELLO,ID 83209
关键词
D O I
10.1137/0727062
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The problems of computing least squares approximations for various types of real and symmetric matrices subject to spectral constraints share a common structure. This paper describes a general procedure in using the projected gradient method. It is shown that the projected gradient of the objective function on the manifold of constraints usually can be formulated explicity. This gives rise to the construction of a descent flow that can be followed numerically. The explicit form also facilitates the computation of the second-order optimality conditions. Examples of applications are discussed. With slight modifications, the procedure can be extended to solve least squares problems for general matrices subject to singular-value constraints.
引用
收藏
页码:1050 / 1060
页数:11
相关论文
共 15 条
[1]  
Arnold V.I., 1988, GEOMETRICAL METHODS
[2]   ISOSPECTRAL FLOWS AND ABSTRACT MATRIX FACTORIZATIONS [J].
CHU, MT ;
NORRIS, LK .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1988, 25 (06) :1383-1391
[3]  
CHU MT, IN PRESS SIAM J MATR
[4]  
DRIESSEL KR, 1987, 8701 ID STAT U DEP M
[5]  
DRIESSEL KR, 1987, 541 CLEMS U DEP MATH
[6]   THE FORMULATION AND ANALYSIS OF NUMERICAL-METHODS FOR INVERSE EIGENVALUE PROBLEMS [J].
FRIEDLAND, S ;
NOCEDAL, J ;
OVERTON, ML .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (03) :634-667
[7]  
Gill P. E., 1981, PRACTICAL OPTIMIZATI
[8]  
Golub G.H., 1996, MATH GAZ, VThird
[9]   THE VARIATION OF THE SPECTRUM OF A NORMAL MATRIX [J].
HOFFMAN, AJ ;
WIELANDT, HW .
DUKE MATHEMATICAL JOURNAL, 1953, 20 (01) :37-39
[10]  
Lancaster P., 1985, COMPUTER SCI APPL MA