Preconditioned conjugate gradient methods for the solution of indefinite least squares problems

The conjugate gradient (CG) method is considered for solving the large and sparse indefinite least squares (ILS) problem min  x ( b − Ax ) T J ( b − Ax ) where J =diag ( I p ,− I q ) is a signature matrix. However the rate of convergence becomes slow for ill-conditioned problems. The QR-based precon...

Full description

Saved in:
Bibliographic Details
Published in:Calcolo 2011-09, Vol.48 (3), p.261-271
Main Authors: Liu, Qiaohua, Li, Xianjuan
Format: Article
Language:English
Subjects:
Conjugate gradient method
Conjugate gradients
Convergence
Least squares method
Linear equations
Mathematical models
Mathematics
Mathematics and Statistics
Numerical Analysis
Signatures
Theory of Computation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The conjugate gradient (CG) method is considered for solving the large and sparse indefinite least squares (ILS) problem min  x ( b − Ax ) T J ( b − Ax ) where J =diag ( I p ,− I q ) is a signature matrix. However the rate of convergence becomes slow for ill-conditioned problems. The QR-based preconditioner is found to be effective in accelerating the convergence. Numerical results show that the sparse Householder QR-based preconditioner is superior to the CG method especially for sparse and ill-conditioned problems.
ISSN:0008-0624
1126-5434
DOI:10.1007/s10092-011-0039-8