NSPCG User's Guide

Version 1.0

A Package for

Solving Large Sparse Linear Systems by

Various Iterative Methods

Thomas C. Oppe

Wayne D. Joubert

David R. Kincaid

April 1988 CNA-216

This work was supported in part by the National Science Foundation under Grant CCR-8518722, the Department of Energy under Grant DE-FG05-87ER25048, and Cray Research, Inc. under Grant LTR DTD with The University of Texas at Austin. Thomas C. Oppe's participation was supported in part by the Control Data Corporation through its PACER Fellowship Program (1985-87) and by Sandia National Laboratory through Contract No. 06-4298 (1987-88).

NSPCG User's Guide ¹
Version 1.0

A Package for
Solving Large Sparse Linear Systems by
Various Iterative Methods

Thomas C. Oppe
Wayne D. Joubert
David R. Kincaid

Center for Numerical Analysis
The University of Texas at Austin

April, 1988

Abstract:

NSPCG (for Nonsymmetric Preconditioned Conjugate Gradient) is a computer package to solve the linear system Au=b by various iterative methods. The coefficient matrix A is assumed to be large and sparse with real coefficients. A wide selection of preconditioners and accelerators is available for both symmetric and nonsymmetric coefficient matrices. Several sparse matrix data structures are available to represent matrices whose structures range from highly structured to completely unstructured.

Disclaimer

The University of Texas at Austin and the Center for Numerical Analysis (CNA) disclaim all warranties with regard to the NSPCG software package, including all warranties of merchantability and fitness, and any stated express warranties are in lieu of all obligations or liability on the part of The University or the CNA for damages, including, but not limited to, special, indirect, or consequential damages arising out of or in connection with the use or performance of NSPCG. In no event will The University or the CNA be liable for any direct, indirect, special, incidental, or consequential damages arising in connection with use of or inability to use NSPCG or the documentation.

It should be emphasized that the NSPCG package is still in preliminary and incomplete form. For example,

• The use of adaptive procedures for $\omega$ in the SOR and SSOR methods assume a symmetric or nearly symmetric matrix. In the nonsymmetric case, the user must supply a good choice of $\omega$ when using SSOR with any of the nonsymmetric accelerators, and this value will not change during the iterations.
• Eigenvalue estimation procedures are available for only certain of the nonsymmetric accelerators.

• Not all accelerators allow right-oriented or split preconditioners.

• Not all preconditioners are available for each of the allowed data structures in NSPCG.

A limited number of copies of the NSPCG package will be made available on request with the understanding that it is intended as a research tool and will undergo further development. The interested reader should write to the address below for additional information on obtaining the distribution tape of the program. Also, reports of difficulties encountered in using the system or comments and suggestions for improving the package would be welcome.

Center for Numerical Analysis

RLM Bldg. 13.150

University of Texas at Austin

Austin, Texas 78713-8510