caa a22 4500 606167323 CHVBK 20210128100702.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10665-013-9656-3 doi (NATIONALLICENCE)springer-10.1007/s10665-013-9656-3 Convergence acceleration of Kaczmarz's method [Elektronische Daten] [Claude Brezinski, Michela Redivo-Zaglia] The method of alternating projections (MAP) is an iterative procedure for finding the projection of a point on the intersection of closed subspaces of a Hilbert space. The convergence of this method is usually slow, and several methods for its acceleration have already been proposed. In this work, we consider a special MAP, namely Kaczmarz's method for solving consistent systems of linear equations. The convergence of this method is discussed. After giving its matrix formulation and its projection properties, we consider several procedures for accelerating its convergence. They are based on sequence transformations whose kernels contain sequences of the same form as the sequence of vectors generated by Kaczmarz's method. Acceleration can be achieved either directly, that is without modifying the sequence obtained by the method, or by restarting it from the vector obtained by acceleration. Numerical examples show the effectiveness of both procedures. Springer Science+Business Media Dordrecht, 2013 Acceleration nationallicence Extrapolation nationallicence Kaczmarz's method nationallicence Linear systems nationallicence Projection method nationallicence Brezinski Claude Laboratoire Paul Painlevé, UMR CNRS 8524, UFR de Mathématiques Pures et Appliquées, Université des Sciences et Technologies de Lille, 59655, Villeneuve d'Ascq Cedex, France aut Redivo-Zaglia Michela Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy aut Journal of Engineering Mathematics Springer Netherlands 93/1(2015-08-01), 3-19 0022-0833 93:1<3 2015 93 10665 https://doi.org/10.1007/s10665-013-9656-3 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/s10665-013-9656-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Brezinski Claude Laboratoire Paul Painlevé, UMR CNRS 8524, UFR de Mathématiques Pures et Appliquées, Université des Sciences et Technologies de Lille, 59655, Villeneuve d'Ascq Cedex, France aut NATIONALLICENCE 700 1- Redivo-Zaglia Michela Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Springer Netherlands 93/1(2015-08-01), 3-19 0022-0833 93:1<3 2015 93 10665