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

Authors:
Qiaohua Liu;Xianjuan Li
Affiliations:
Department of Mathematics, Shanghai University, Shanghai, China;Department of Mathematics, Shanghai University, Shanghai, China
Venue:
Calcolo: a quarterly on numerical analysis and theory of computation
Year:
2011

Citing 4
Cited 0

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Abstract

The conjugate gradient (CG) method is considered for solving the large and sparse indefinite least squares (ILS) problem min驴 x (b驴Ax) T J(b驴Ax) where J=diag驴(I p ,驴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.