Naslov
Adapting the Kogbetliantz Method to Shared Memory Machines

Autori
Hari, Vjeran ; Zadelj-Martić, Vida

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Applied Mathematics and Scientific Computing / - Zagreb, 2007, 24-25

Skup
Applied Mathematics and Scientific Computing

Mjesto i datum
Brijuni, Hrvatska, 09.07.2007. - 13.07.2007

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Kogbetliantz method; parallel computing

Sažetak
Typical fast SVD solvers for general matrices, like Divide and Conquer, Differential QED and the QR method, first reduce the initial matrix to bidiagonal form. It is known that this initial reduction can deteriorate the relative accuracy of the smallest singular values even if the initial matrix is well-behaved for accurate SVD computation. For such matrices, the one-sided Jacobi methods have proved to be very accurate and the latest research indicates that they can be made fast. Since they possess intrinsic parallelism, they are fast and accurate on standard and parallel computers. In this report, we pay attention to the less known two-sided Jacobi-type method, the Kogbetliantz method. Recent research of Matejaš and Hari, and Londre and Rhee prove that this method is relatively accurate. When compared with the one-sided methods, the Kogbetliantz method has certain advantages (almost diagonal matrix is further diagonalized, it uses sound stopping criterion \ldots ) and disadvantages (left transformations are slow, it requires more memory space \ldots ). The Kogbetliantz method is the most efficient and accurate for nearly diagonal triangular matrices. Here, we present an adaptation of the Kogbetliantz method for work with shared memory machines. It essentially preserves the (initially created) zero elements, which has beneficial impact to its simplicity and to the quadratic asymptotic convergence. The method can be further modified to work with blocks, which leads to the better usage of contemporary processor capabilities like the cache memory. In addition, the slowdown coming from the left transformations can be essentially reduced.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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