caa a22 4500 463170040 CHVBK 20180406164810.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s10957-006-9119-3 doi (NATIONALLICENCE)springer-10.1007/s10957-006-9119-3 Fasano G. Istituto di Analisi dei Sistemi ed Informatica A. Ruberti, CNR, Rome, Italy aut Lanczos Conjugate-Gradient Method and Pseudoinverse Computation on Indefinite and Singular Systems [Elektronische Daten] [G. Fasano] This paper extends some theoretical properties of the conjugate gradient-type method FLR (Ref. 1) for iteratively solving indefinite linear systems of equations. The latter algorithm is a generalization of the conjugate gradient method by Hestenes and Stiefel (CG, Ref. 2). We develop a complete relationship between the FLR algorithm and the Lanczos process, in the case of indefinite and possibly singular matrices. Then, we develop simple theoretical results for the FLR algorithm in order to construct an approximation of the Moore-Penrose pseudoinverse of an indefinite matrix. Our approach supplies the theoretical framework for applications within unconstrained optimization. Springer Science + Business Media, Inc., 2006 Unconstrained optimization nationallicence Krylov subspace methods nationallicence planar conjugate gradient nationallicence Moore-Penrose pseudoinverse nationallicence Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/2(2007-02-01), 267-285 0022-3239 132:2<267 2007 132 10957 https://doi.org/10.1007/s10957-006-9119-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-006-9119-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Fasano G. Istituto di Analisi dei Sistemi ed Informatica A. Ruberti, CNR, Rome, Italy aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/2(2007-02-01), 267-285 0022-3239 132:2<267 2007 132 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer