On Kaczmarz's projection iteration as a direct solver for linear least squares problems

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autor(en): Popa C, Preclik T, Köstler H, Rüde U
Zeitschrift: Linear Algebra and Its Applications
Verlag: Elsevier
Jahr der Veröffentlichung: 2012
Band: 436
Heftnummer: 2
Seitenbereich: 389-404
ISSN: 0024-3795


Abstract

In this paper we construct and theoretically analyze a class of direct projection algorithms for the numerical solution of linear least squares problems. These algorithms are obtained by adding supplementary directions for projection, constructed as linear combinations of the initial system rows and columns, in Kaczmarz and Extended Kaczmarz iterative methods. The above ideas are extended to the block row and column versions of the previously mentioned methods. The developed algorithms are then compared with other direct projection-based methods by the application to problems arising in multibody elasticity. © 2010 Elsevier Inc. All rights reserved.


FAU-Autoren / FAU-Herausgeber

Köstler, Harald PD Dr.
Lehrstuhl für Informatik 10 (Systemsimulation)
Preclik, Tobias Dr.-Ing.
Lehrstuhl für Informatik 10 (Systemsimulation)
Rüde, Ulrich Prof. Dr.
Lehrstuhl für Informatik 10 (Systemsimulation)


Zitierweisen

APA:
Popa, C., Preclik, T., Köstler, H., & Rüde, U. (2012). On Kaczmarz's projection iteration as a direct solver for linear least squares problems. Linear Algebra and Its Applications, 436(2), 389-404. https://dx.doi.org/10.1016/j.laa.2011.02.017

MLA:
Popa, Constantin, et al. "On Kaczmarz's projection iteration as a direct solver for linear least squares problems." Linear Algebra and Its Applications 436.2 (2012): 389-404.

BibTeX: 

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