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Novel Modifications of Parallel Jacobi Algorithms


Singer, Sanja; Singer, Saša; Novaković, Vedran; Ušćumlić, Aleksandar; Dunjko, Vedran
Novel Modifications of Parallel Jacobi Algorithms // Numerical algorithms, 59 (2012), 1; 1-27 doi:10.1007/s11075-011-9473-6 (međunarodna recenzija, članak, znanstveni)


Naslov
Novel Modifications of Parallel Jacobi Algorithms

Autori
Singer, Sanja ; Singer, Saša ; Novaković, Vedran ; Ušćumlić, Aleksandar ; Dunjko, Vedran

Izvornik
Numerical algorithms (1017-1398) 59 (2012), 1; 1-27

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Hermitian matrices; eigenvalues; Jacobi algorithm; parallelization

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Računarstvo



POVEZANOST RADA


Projekt / tema
037-1193086-2771 - Numeričke metode u geofizičkim modelima (Saša Singer, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


Uključenost u ostale bibliografske baze podataka:


  • Compu-Math Citation Index
  • INSPEC
  • MathSciNet
  • Zentrallblatt für Mathematik/Mathematical Abstracts
  • Scopus
  • Academic OneFile
  • ACM Digital Library
  • Computer Abstracts
  • Computer Science Index
  • Current Abstracts
  • DBLP
  • Digital Mathematics Registry
  • International Abstracts in Operations Research
  • OCLC
  • Summon by Serial Solutions
  • VINITI


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