On a regularization technique for Kovarik-like approximate orthogonalization algorithms

Journal article


Publication Details

Author(s): Nicola A, Popa C, Rüde U
Journal: Carpathian Journal of Mathematics
Publisher: Department of Mathematics and Computer Science North University of Baia Mare
Publication year: 2011
Volume: 27
Journal issue: 1
Pages range: 114-122
ISSN: 1584-2851


Abstract

In this paper we consider four versions of Kovarik's iterative orthogonalization algorithm, for approximating the minimal norm solution of symmetric least squares problems. Although the theoretical convergence rate of these algorithms is at least linear, in practical applications we observed that a too big number of iterations can dramatically deteriorate the already obtained approximation. In this respect we analyse the above mentioned Kovarik-like methods according to the modifications they make on the "machine zero" eigenvalues of the problem's (symmetric) matrix. We establish a theoretical almost optimal formula for the number of iterations necessary to obtain an enough accurate approximation, as well as to avoid the above mentioned troubles. Experiments on collocation discretization of a Fredholm first kind integral equation illustrate the efficiency of our considerations.


FAU Authors / FAU Editors

Rüde, Ulrich Prof. Dr.
Lehrstuhl für Informatik 10 (Systemsimulation)


How to cite

APA:
Nicola, A., Popa, C., & Rüde, U. (2011). On a regularization technique for Kovarik-like approximate orthogonalization algorithms. Carpathian Journal of Mathematics, 27(1), 114-122.

MLA:
Nicola, A., Constantin Popa, and Ulrich Rüde. "On a regularization technique for Kovarik-like approximate orthogonalization algorithms." Carpathian Journal of Mathematics 27.1 (2011): 114-122.

BibTeX: 

Last updated on 2018-26-09 at 10:08