Solving linearly constrained matrix least squares problem by LSQR

被引：7

作者：

Qiu, Yuyang ^{[1
]}

Wang, Anding ^{[2
]}

机构：

[1] Zhejiang Gongshang Univ, Coll Stat & Math, Hangzhou 310018, Zhejiang, Peoples R China

[2] Zhejiang Gongshang Univ, Coll Informat & Elect, Hangzhou 310018, Zhejiang, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 236卷

基金：

中国国家自然科学基金;

关键词：

Matrix iterative algorithm; LSQR; Least squares problem; Constraint matrix; Coordinate mapping; Matrix-form iteration; SYMMETRIC SOLUTION; ITERATIVE METHOD; EQUATION AXB;

D O I：

10.1016/j.amc.2014.02.073

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Matrix iterative algorithm LSQR is proposed for solving the linearly constrained matrix least squares (LS) problem. With the special properties of constraint matrix, Kronecker product and the coordinate mapping from the constrained space to its (independent) parameter space, we transform the constrained matrix LS problem to the unconstrained long vector least squares problem and rewrite the corresponding vector-form algorithm back to the matrix one. The resulting matrix-form iteration only consists of matrix-matrix product and does not involve the Kronecker product. Numerical results are reported to show the feasibility of the proposed method. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：273 / 286

页数：14

共 50 条

[41] Solving large-scale constrained least-squares problems
Abdel-Aziz, MR
El-Alem, MM
APPLIED MATHEMATICS AND COMPUTATION, 2003, 137 (2-3) : 571 - 587
[42] STABLE METHOD FOR SOLVING CERTAIN CONSTRAINED LEAST-SQUARES PROBLEMS
MIFFLIN, R
MATHEMATICAL PROGRAMMING, 1979, 16 (02) : 141 - 158
[43] Equality constrained least squares problem over quaternion field
Jiang, TS
Wei, MS
APPLIED MATHEMATICS LETTERS, 2003, 16 (06) : 883 - 888
[44] Localization with TOA as a Constrained Robust Stochastic Least Squares Problem
Korkmaz, Sayit
van der Veen, Alle-Jan
2008 IEEE INTERNATIONAL CONFERENCE ON ULTRA-WIDEBAND, VOL 1, PROCEEDINGS, 2008, 1 : 197 - 200
[45] The equality constrained indefinite least squares problem: Theory and algorithms
Bojanczyk, A
Higham, NJ
Patel, H
BIT NUMERICAL MATHEMATICS, 2003, 43 (03) : 505 - 517
[46] Algebraic Method for Inequality Constrained Quaternion Least Squares Problem
Sitao Ling
Xiangjian Xu
Tongsong Jiang
Advances in Applied Clifford Algebras, 2013, 23 : 919 - 928
[47] The Equality Constrained Indefinite Least Squares Problem: Theory and Algorithms
Adam Bojanczyk
Nicholas J. Higham
Harikrishna Patel
BIT Numerical Mathematics, 2003, 43 : 505 - 517
[48] ON THE CONSTRAINED LINEAR LEAST-SQUARES PROBLEM - A PERSONAL VIEW
HANSON, RJ
APPLIED NUMERICAL MATHEMATICS, 1987, 3 (05) : 443 - 452
[49] A new technique of quaternion equality constrained least squares problem
Jiang, Tongsong
Zhao, Jianli
Wei, Musheng
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 216 (02) : 509 - 513
[50] Algebraic Method for Inequality Constrained Quaternion Least Squares Problem
Ling, Sitao
Xu, Xiangjian
Jiang, Tongsong
ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2013, 23 (04) : 919 - 928

← 1 2 3 4 5 →