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

Popa C, Preclik T, Köstler H, Rüde U (2012)

Publication Type: Journal article

Publication year: 2012

Journal

Linear Algebra and Its Applications Elsevier

Publisher: Elsevier

Book Volume: 436

Pages Range: 389-404

Journal Issue: 2

DOI: 10.1016/j.laa.2011.02.017

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.

Authors with CRIS profile

Tobias Preclik Lehrstuhl für Informatik 10 (Systemsimulation) Harald Köstler Lehrstuhl für Informatik 10 (Systemsimulation) Ulrich Rüde Lehrstuhl für Informatik 10 (Systemsimulation)

Related research project(s)

The pe Rigid Body Physics Engine (PE) Jan. 1, 2006 - Jan. 1, 2009

How to cite

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.

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