Preconditioned conjugate gradient algorithms and software for solving large sparse linear systems
The classical form of the conjugate gradient method (CG method), developed by Hestenes and Stiefel, for solving the linear system Au = b is applicable when the coefficient matrix A is symmetric and positive definite (SPD). In this paper we consider various alternative forms of the CG method as well as generalizations to cases where A is not necessarily SPD. This analysis includes the ''preconditioned conjugate gradient method'' which is equivalent to conjugate gradient acceleration of a basic iterative method corresponding to a preconditioned system. Both the symmetrizable case and the nonsymmetrizable case are considered. For the nonsymmetrizable case there are very few useful theoretical results available. A package of programs, known as ITPACK, has been developed as a tool for carrying out experimental studies on various algorithms. Preliminary conclusions based on experimental results are given. 42 refs.
- Research Organization:
- Texas Univ., Austin (USA). Center for Numerical Analysis
- DOE Contract Number:
- AS05-81ER10954
- OSTI ID:
- 5383477
- Report Number(s):
- CONF-8608206-1-Draft; CNA-207; ON: DE88002180
- Country of Publication:
- United States
- Language:
- English
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