By Topic

A unified theory for Krylov algorithms

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Gang Xie ; Inst. of Comput. Applications, CAEP, China

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.

Published in:

Algorithms and Architectures for Parallel Processing, 2002. Proceedings. Fifth International Conference on

Date of Conference:

23-25 Oct. 2002