On a regularization technique for Kovarik-like approximate orthogonalization algorithms

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autor(en): Nicola A, Popa C, Rüde U
Zeitschrift: Carpathian Journal of Mathematics
Verlag: Department of Mathematics and Computer Science North University of Baia Mare
Jahr der Veröffentlichung: 2011
Band: 27
Heftnummer: 1
Seitenbereich: 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-Autoren / FAU-Herausgeber

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


Zitierweisen

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.

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Zuletzt aktualisiert 2018-26-09 um 10:08