Pregled bibliografske jedinice broj: 169259
Accelerating Block-Jacobi Methods
Accelerating Block-Jacobi Methods // Guaranteed Error-Bounds for the Solution of Nonlinear Problems in Applied Mathematics. / Herzberger J. (ur.).
München: GAMM, 2003. str. 6-6 (predavanje, međunarodna recenzija, sažetak, znanstveni)
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Naslov
Accelerating Block-Jacobi Methods
Autori
Hari, Vjeran
Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni
Izvornik
Guaranteed Error-Bounds for the Solution of Nonlinear Problems in Applied Mathematics.
/ Herzberger J. - München : GAMM, 2003, 6-6
Skup
Guaranteed Error-Bounds for the Solution of Nonlinear Problems in Applied Mathematics.
Mjesto i datum
München, Njemačka, 01.09.2003. - 05.09.2003
Vrsta sudjelovanja
Predavanje
Vrsta recenzije
Međunarodna recenzija
Ključne riječi
Block-Jacobi methods
Sažetak
Until recently QR methods and their variations have been considered as the fastest methods for computing the singular value and the symmetric eigenvalue problems. Lately, Divide and Conquer methods have developed to a stage at which for larger matrices they overcome the performance of the QR methods. However, the both types of methods, require reducing the initial full matrix to bidiagonal (tridiagonal in case of eigenvalue problem) form. This preprocessing can deteriorate accuracy of smaller singular values (eigenvalues). In addition, reduction to bidiagonal (tridiagonal) form is getting costly since the later part of the QR and DC methods is getting faster through newer variations (e.g.\ DQD+inverse iteration). The third type methods are diagonalization or Jacobi methods. They are very accurate as they can deliver all output data to the accuracy that is allowed by the problem. However, for larger matrices, Jacobi methods are generally considered to be several times slower than the appropriate QR methods. The aim of this communication is to give a closer look at the latest developments in accelerating one-sided Jacobi methods and to show that the newest variations of one-sided Jacobi methods are as fast as the fastest QR methods. In order to further enhance efficiency, block versions of these methods have been designed. It is shown how CS decomposition and some other tricks can be used to reduce the flop count in the slowest part of the algorithm -- updating the block columns.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
