An algorithm for solving the indefinite least squares problem with equality constraints

被引：16

作者：

Mastronardi, Nicola ^{[1
]}

Van Dooren, Paul ^{[2
]}

机构：

[1] CNR, Ist Applicaz Calcolo M Picone, I-70126 Bari, Italy

[2] Catholic Univ Louvain, Dept Engn Math, B-1348 Louvain, Belgium

来源：

BIT NUMERICAL MATHEMATICS | 2014年 / 54卷 / 01期

关键词：

Indefinite matrix; Indefinite least squares; Equality constraints;

D O I：

10.1007/s10543-013-0452-2

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

An algorithm for computing the solution of indefinite least squares problems and of indefinite least squares problems with equality constrained is presented. Such problems arise when solving total least squares problems and in H (a)-smoothing. The proposed algorithm relies only on stable orthogonal transformations reducing recursively the associated augmented matrix to proper block anti-triangular form. Some numerical results are reported showing the properties of the algorithm.

引用

页码：201 / 218

页数：18

共 14 条

[1] The equality constrained indefinite least squares problem: Theory and algorithms
Bojanczyk, A
Higham, NJ
Patel, H
[J]. BIT NUMERICAL MATHEMATICS, 2003, 43 (03) : 505 - 517
[2] Solving the indefinite least squares problem by hyperbolic QR factorization
Bojanczyk, A
Higham, NJ
Patel, H
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2003, 24 (04) : 914 - 931
[3] A stable and efficient algorithm for the indefinite linear least-squares problem
Chandrasekaran, S
Gu, M
Sayed, AH
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1998, 20 (02) : 354 - 362
[4] Golub G. H., 1996, MATRIX COMPUTATIONS
[5] AN ANALYSIS OF THE TOTAL LEAST-SQUARES PROBLEM
GOLUB, GH
VANLOAN, CF
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1980, 17 (06) : 883 - 893
[6] ON PRACTICAL CONDITIONS FOR THE EXISTENCE AND UNIQUENESS OF SOLUTIONS TO THE GENERAL EQUALITY QUADRATIC-PROGRAMMING PROBLEM
GOULD, NIM
[J]. MATHEMATICAL PROGRAMMING, 1985, 32 (01) : 90 - 99
[7] Linear estimation in Krein spaces .1. Theory
Hassibi, B
Sayed, AH
Kailath, T
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1996, 41 (01) : 18 - 33
[8] J-orthogonal matrices:: Properties and generation
Higham, NJ
[J]. SIAM REVIEW, 2003, 45 (03) : 504 - 519
[9] The hyperbolic elimination method for solving the equality constrained indefinite least squares problem
Liu, Qiaohua
Pan, Baozhen
Wang, Qian
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (13) : 2953 - 2966
[10] Algebraic properties and perturbation results for the indefinite least squares problem with equality constraints
Liu, Qiaohua
Wang, Minghui
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (02) : 425 - 434

← 1 2 →