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

Journal article


Publication Details

Author(s): Popa C, Preclik T, Köstler H, Rüde U
Journal: Linear Algebra and Its Applications
Publisher: Elsevier
Publication year: 2012
Volume: 436
Journal issue: 2
Pages range: 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 Authors / FAU Editors

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


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.

BibTeX: 

Last updated on 2018-09-12 at 13:50