caa a22 4500 606167390 CHVBK 20210128100702.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10665-013-9677-y doi (NATIONALLICENCE)springer-10.1007/s10665-013-9677-y Vector extrapolation applied to truncated singular value decomposition and truncated iteration [Elektronische Daten] [A. Bouhamidi, K. Jbilou, L. Reichel, H. Sadok, Z. Wang] This paper is concerned with the computation of accurate approximate solutions of linear systems of equations and linear least-squares problems with a very ill-conditioned matrix and error-contaminated data. The solution of these kinds of problems requires regularization. Common regularization methods include truncated singular value decomposition (TSVD) and truncated iteration with a Krylov subspace method. It can be difficult to determine when to truncate. Recently, it has been demonstrated that extrapolation of approximate solutions determined by TSVD gives a new sequence of approximate solutions that is less sensitive to errors in data than the original approximate solutions. The present paper describes a novel approach to determining a suitable truncation index by comparing the original and extrapolated approximate solutions. Applications to TSVD and the LSQR iterative method are presented. Springer Science+Business Media Dordrecht, 2014 Discrete ill-posed problem nationallicence LSQR nationallicence Truncation criterion nationallicence Truncated iteration nationallicence Truncated singular value decomposition nationallicence Vector extrapolation nationallicence Bouhamidi A. Laboratoire de Mathématiques Pures et Appliquées, Centre Universtaire de la Mi-Voix, Université du Littoral, Batiment H. Poincarré, 50 Rue F. Buisson, BP 699, 62228, Calais Cedex, France aut Jbilou K. Laboratoire de Mathématiques Pures et Appliquées, Centre Universtaire de la Mi-Voix, Université du Littoral, Batiment H. Poincarré, 50 Rue F. Buisson, BP 699, 62228, Calais Cedex, France aut Reichel L. Department of Mathematical Sciences, Kent State University, 44242, Kent, OH, USA aut Sadok H. Laboratoire de Mathématiques Pures et Appliquées, Centre Universtaire de la Mi-Voix, Université du Littoral, Batiment H. Poincarré, 50 Rue F. Buisson, BP 699, 62228, Calais Cedex, France aut Wang Z. Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, No 29 Yudao Street, 210016, Nanjing, People's Republic of China aut Journal of Engineering Mathematics Springer Netherlands 93/1(2015-08-01), 99-112 0022-0833 93:1<99 2015 93 10665 https://doi.org/10.1007/s10665-013-9677-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10665-013-9677-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bouhamidi A. Laboratoire de Mathématiques Pures et Appliquées, Centre Universtaire de la Mi-Voix, Université du Littoral, Batiment H. Poincarré, 50 Rue F. Buisson, BP 699, 62228, Calais Cedex, France aut NATIONALLICENCE 700 1- Jbilou K. Laboratoire de Mathématiques Pures et Appliquées, Centre Universtaire de la Mi-Voix, Université du Littoral, Batiment H. Poincarré, 50 Rue F. Buisson, BP 699, 62228, Calais Cedex, France aut NATIONALLICENCE 700 1- Reichel L. Department of Mathematical Sciences, Kent State University, 44242, Kent, OH, USA aut NATIONALLICENCE 700 1- Sadok H. Laboratoire de Mathématiques Pures et Appliquées, Centre Universtaire de la Mi-Voix, Université du Littoral, Batiment H. Poincarré, 50 Rue F. Buisson, BP 699, 62228, Calais Cedex, France aut NATIONALLICENCE 700 1- Wang Z. Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, No 29 Yudao Street, 210016, Nanjing, People's Republic of China aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Springer Netherlands 93/1(2015-08-01), 99-112 0022-0833 93:1<99 2015 93 10665