Novel Modifications of Parallel Jacobi Algorithms

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

doi:10.1007/s11075-011-9473-6

Pregled bibliografske jedinice broj: 513365

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)

CROSBI ID: 513365 Za ispravke kontaktirajte CROSBI podršku putem web obrasca

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

Projekti:
037-1193086-2771 - Numeričke metode u geofizičkim modelima (Singer, Saša, MZOS ) ( CroRIS)

Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Profili:

Sanja Singer (autor)