DocumentCode :
3091417
Title :
A unified theory for Krylov algorithms
Author :
Xie, Gang
Author_Institution :
Inst. of Comput. Applications, CAEP, China
fYear :
2002
fDate :
23-25 Oct. 2002
Firstpage :
71
Lastpage :
75
Abstract :
Large systems of linear equations arise in many different scientific applications. For example, partial differential equations discretized with the finite difference or finite element method yield a system of equations. Large systems can be solved with either sparse factorization techniques or iterative methods. These two approaches can be combined into a method that uses approximate factorization preconditioning for an iterative method. Krylov algorithms are iterative numerical methods for large unsymmetric systems of linear equations. In this paper, we set up a general theoretical framework for Krylov algorithms and so highlight their common features. We first introduce the conception of orthogonality between linear subspaces. We then formulate a unified definition for Krylov algorithms. On this basis, we study some of their common properties. This work may give useful hints on formulating new better iterative methods for unsymmetric problems.
Keywords :
equations; iterative methods; natural sciences computing; Krylov algorithms; approximate factorization preconditioning; finite difference method; finite element method; iterative numerical methods; large unsymmetric linear equation systems; linear subspaces; orthogonality; partial differential equations; scientific applications; sparse factorization techniques; unified theory; Application software; Computer applications; Difference equations; Differential equations; Finite difference methods; Finite element methods; Gradient methods; Iterative algorithms; Iterative methods; Partial differential equations;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Algorithms and Architectures for Parallel Processing, 2002. Proceedings. Fifth International Conference on
Conference_Location :
Beijing, China
Print_ISBN :
0-7695-1512-6
Type :
conf
DOI :
10.1109/ICAPP.2002.1173554
Filename :
1173554
Link To Document :
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