The search for omega
- Texas Univ., Austin, TX (USA). Center for Numerical Analysis
- Alabama Univ., University, AL (USA). Dept. of Mathematics
For the effective use of iterative algorithms for solving large sparse linear systems it is often necessary to select certain iteration parameters. Examples of iteration parameters are the relaxation factor, omega, for the SOR and SSOR methods and the largest and smallest eigenvalues of the matrix for a basic iterative method when Chebyshev acceleration is used to speed up the convergence. For many iterative algorithms the performance is extremely sensitive to the choice of iteration parameters. Moreover, uncertainty as to how to choose iteration parameters has often, in the past, tended to discourage the use of iterative methods, as opposed to direct methods, for certain classes of problems. The purpose of this paper is to review the development of procedures for choosing iteration parameters, with special emphasis on methods applicable to linear systems arising from the numerical solution of partial differential equations. The discussion will include a priori procedures including analytic techniques, spectral methods, and methods based on related differential equations. Automatic, or adaptive,'' procedures, wherein the iteration parameters are improved as the computation proceeds, will also be discussed. Some of these procedures have been incorporated into the ITPACK software packages for solving large sparse linear systems. Numerical experiments indicate that the amount of overhead needed to determine satisfactory parameters is usually not excessive. Methods for choosing iteration parameters for nonsymmetric systems will also be considered.
- Research Organization:
- Texas Univ., Austin, TX (USA). Center for Numerical Analysis
- Sponsoring Organization:
- USDOD; DOE/ER; National Science Foundation (NSF)
- DOE Contract Number:
- FG05-87ER25048
- OSTI ID:
- 7092941
- Report Number(s):
- CONF-8810515-2; CNA-223; ON: DE90013963; CNN: DCR-8518722; AFOSR-85-0052
- Resource Relation:
- Conference: Conference on iterative methods for large linear systems, Austin, TX (USA), 19-21 Oct 1988
- Country of Publication:
- United States
- Language:
- English
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