caa a22 4500 445862106 CHVBK 20180317145446.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s10092-011-0039-8 doi (NATIONALLICENCE)springer-10.1007/s10092-011-0039-8 Preconditioned conjugate gradient methods for the solution of indefinite least squares problems [Elektronische Daten] [Qiaohua Liu, Xianjuan Li] 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. Springer-Verlag, 2011 Indefinite least squares problems nationallicence Preconditioner nationallicence Conjugate gradient method nationallicence Sparse QR factorization nationallicence Liu Qiaohua Department of Mathematics, Shanghai University, Shanghai, China aut Li Xianjuan Department of Mathematics, Shanghai University, Shanghai, China aut Calcolo Springer Milan 48/3(2011-09-01), 261-271 0008-0624 48:3<261 2011 48 10092 https://doi.org/10.1007/s10092-011-0039-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10092-011-0039-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Liu Qiaohua Department of Mathematics, Shanghai University, Shanghai, China aut NATIONALLICENCE 700 1- Li Xianjuan Department of Mathematics, Shanghai University, Shanghai, China aut NATIONALLICENCE 773 0- Calcolo Springer Milan 48/3(2011-09-01), 261-271 0008-0624 48:3<261 2011 48 10092 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer