- Tytuł:
- The non-symmetric s-step Lanczos algorithm: Derivation of efficient recurrences and synchronization-reducing variants of BiCG and QMR
- Autorzy:
-
Feuerriegel, S.
Bücker, H. M. - Powiązania:
- https://bibliotekanauki.pl/articles/331344.pdf
- Data publikacji:
- 2015
- Wydawca:
- Uniwersytet Zielonogórski. Oficyna Wydawnicza
- Tematy:
-
synchronization reducing
s-step Lanczos
s-step BiCG
s-step QMR
efficient recurrences - Opis:
- The Lanczos algorithm is among the most frequently used iterative techniques for computing a few dominant eigenvalues of a large sparse non-symmetric matrix. At the same time, it serves as a building block within biconjugate gradient (BiCG) and quasi-minimal residual (QMR) methods for solving large sparse non-symmetric systems of linear equations. It is well known that, when implemented on distributed-memory computers with a huge number of processes, the synchronization time spent on computing dot products increasingly limits the parallel scalability. Therefore, we propose synchronization-reducing variants of the Lanczos, as well as BiCG and QMR methods, in an attempt to mitigate these negative performance effects. These so-called s-step algorithms are based on grouping dot products for joint execution and replacing time-consuming matrix operations by efficient vector recurrences. The purpose of this paper is to provide a rigorous derivation of the recurrences for the s-step Lanczos algorithm, introduce s-step BiCG and QMR variants, and compare the parallel performance of these new s-step versions with previous algorithms.
- Źródło:
-
International Journal of Applied Mathematics and Computer Science; 2015, 25, 4; 769-785
1641-876X
2083-8492 - Pojawia się w:
- International Journal of Applied Mathematics and Computer Science
- Dostawca treści:
- Biblioteka Nauki
Artykuł