Novel modifications of parallel Jacobi algorithms

Singer, Sanja and Singer, Saša and Novaković, Vedran and Ušćumlić, Aleksandar and Dunjko, Vedran (2012) Novel modifications of parallel Jacobi algorithms. = Novel modifications of parallel Jacobi algorithms. Numerical Algorithms, 59 (1). pp. 1-27. ISSN 1017-1398. Vrsta rada: ["eprint_fieldopt_article_type_article" not defined]. Kvartili JCR: Q2 (2012). .

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Abstract

We describe two main classes of one-sided trigonometric and hyperbolic Jacobi-type algorithms for computing eigenvalues and eigenvectors of Hermitian matrices. These types of algorithms exhibit significant advantages over many other eigenvalue algorithms. If the matrices permit, both types of algorithms compute the eigenvalues and eigenvectors with high relative accuracy. We present novel parallelization techniques for both trigonometric and hyperbolic classes of algorithms, as well as some new ideas on how pivoting in each cycle of the algorithm can improve the speed of the parallel one-sided algorithms. These parallelization approaches are applicable to both distributed-memory and shared-memory machines. The numerical testing performed indicates that the hyperbolic algorithms may be superior to the trigonometric ones, although, in theory, the latter seem more natural. © 2011 Springer Science+Business Media, LLC.

Item Type: Article (["eprint_fieldopt_article_type_article" not defined])
Keywords (Croatian): Eigenvalues; Hermitian matrices; Jacobi algorithm; Parallelization
Subjects: NATURAL SCIENCES > Mathematics
TECHNICAL SCIENCE
Divisions: 1500 Chair of Mathematics
Indexed in Web of Science: Yes
Indexed in Current Contents: Yes
Citations JCR: 4 (27.4.2015.)
Quartiles: Q2 (2012)
Citations SCOPUS: 3 (27.4.2015.)
Date Deposited: 27 Apr 2015 09:15
Last Modified: 23 May 2017 11:20
URI: http://repozitorij.fsb.hr/id/eprint/3976

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