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SCSL User's Guide
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About This Guide

This publication describes the SGI Scientific Computing Software Library (SCSL) which runs on SGI IRIX and Linux systems. The information in this manual supplements the man pages provided with the SCSL release.

This document is a user's guide for programmers. Readers should have a working knowledge of the IRIX and Linux operating systems, have an understanding of the Fortran and C programming languages, and have a working familiarity with scientific and mathematical theories.

Related publications

The following publications provide information that can supplement the information in this document.

Release notes for Linux systems are stored in /usr/share/doc/sgi-scsl- versionnumber/README.relnotes.

Tuning and Application Guides

The following documents provide information about the applications used on IRIX and Linux systems and about tuning issues on those systems:

Origin 2000 and Onyx2 Performance Tuning and Optimization Guide
Linux Application Tuning Guide
MIPSpro Fortran 77 Programmer's Guide
MIPSpro Fortran 90 Commands and Directives Reference Manual
C++ Programmer's Guide
Guide to SGI Compilers and Compiling Tools
ProDev WorkShop: Overview

The following documentation is provided for the compilers and performance tools which run on SGI Linux systems:

http://sources.redhat.com/gdb/onlinedocs/gdb_toc.html
http://intel.com/software/perflib ; documentation for Intel compiler products can be downloaded from this website.
http://developer.intel.com/software/products/vtune/vtune61/index.htm/
Information about the OpenMP Standard can be found at http://www.openmp.org/specs.

Third Party Documentation

The following publications provide detailed information about the topics discussed in this manual. In many cases, these documents are referenced specifically in this manual.

Anderson, E., Z. Bai, et al. LAPACK User's Guide. Philadelphia SIAM, 1999. This manual is available online at http://www.netlib.org/lapack/lug/index.html .
Anderson, Edward, Jack Dongarra, and Susan Blackford. Installation guide for LAPACK. LAPACK Working Note 41, Technical Report CS-91-138. University of Tennessee (Feb. 1992).
Argham, Nicolas J. Accuracy and Stability of Numeric Algorithms. Philadelphia SIAM, 1996.
Arioli, M., J. W. Demmel, and I. S. Duff. Solving sparse linear systems with sparse backward error. SIAM J. Matrix Anal. Appl. 10 (1989).
Ashcraft, Cleve. A vector implementation of the multifrontal method for large sparse, symmetric positive definite linear systems. Technical Report ETA-TR-51. Boeing Computer Services, 1987.
Duff, I. S., A. M. Erisman, and J. K. Reid. Direct Methods for Sparse Matrices. Monographs on Numerical Analysis. New York: Oxford University Press, 1986.
George, Alan and Joseph W-H Liu. Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall Series in Computational Mathematics. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1981.
Golub, Gene and James M. Ortega. Scientific Computing: An Introduction with Parallel Computing. Boston: Academic Press, 1993.
Golub, Gene H. and Charles F. Van Loan. Matrix Computations. 2nd edition. Baltimore, Maryland: Johns Hopkins University Press, 1989.
Hageman, Louis A. and David M. Young. Applied Iterative Methods. Computer Science and Applied Mathematics. New York and London: Academic Press, 1981.
Heroux, Michael A. A reverse communication interface for ``matrix-free'' preconditioned iterative solvers. Edited by C.A. Brebbia, D. Howard, and A. Peters In Applications of Supercomputers in Engineering II, 207-213. Boston: Computational Mechanics Publications, 1991.
Heroux, Michael A., Phuong Vu, and Chao Wu Yang. A parallel preconditioned conjugate gradient package for solving sparse linear systems on a Cray Y-MP. Applied Numerical Mathematics, 8 (1991).
Hestenes, M. R. and E. Stiefel. Methods of conjugate gradients for solving linear systems. J. Res. National Bureau of Standards 49 (1952): 409-436.
Kincaid, David R., Thomas C. Oppe, John R. Respess, and David M. Young. ITPACKV 2C User's Guide. Technical Report CNA-191. The University of Texas at Austin: Center for Numerical Analysis, (Nov. 1984).
Manteuffel, T. A. An incomplete factorization technique for positive definite linear systems. Math. Comp. 34 (1980): 473-497.
Oppe, Thomas C., Wayne D. Joubert, and David R. Kincaid. NSPCG User's Guide. The University of Texas at Austin: Center for Numerical Analysis, (Dec. 1988).
Reid, J. K., editor. On the Method of Conjugate Gradients for the Solution of Large Sparse Systems of Linear Equations. Large Sparse Sets of Linear Equations, Academic Press, 1971.
Saad, Youcef. Practical use of polynomial preconditionings for the conjugate gradient method., 6(4) (Oct. 1985): 865-881.
Saad, Youcef and Martin H. Schultz. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal of Scientific and Statistical Computing, 7(3) (Jul. 1986): 856-869.
Sonneveld, Peter. CGS, a fast lanczos-type solver for nonsymmetric linear systems. SIAM Journal of Scientific and Statistical Computing, 10(1) (Jan. 1989): 36-52.
Stewart, G. W. Introduction to Matrix Computations . Orlando, Florida: Academic Press, 1973.
Wilkinson, J. H. The Algebraic Eigenvalue Problem . Oxford, England: Oxford University Press, 1965.
Yang, Chao W. A parallel multifrontal method for sparse symmetric definite linear systems on the Cray Y-MP. Proceedings of the Fifth SIAM Conference on Parallel Processing for Scientific Computing . Houston, Texas (Apr. 1992).

You can find a good general reference on the solution of sparse linear systems in Golub and Van Loan. You can find a good introduction to direct and iterative methods, as well as methods for special linear systems, in these texts. See the special section of the November 1989 issue of the SIAM Journal of Scientific and Statistical Computing , pages 1135-1232 for an updated general reference.

See George and Liu, Duff and Erisman, and Reid for classical references that give a thorough and in-depth treatment of sparse direct solvers. Another common reference is Ashcraft.

The original conjugate gradient algorithm was presented in Hestenes and Stiefel; however, Reid presented the first practical application. A classical text in iterative methods is that of Hageman and Young. You can find good discussions of the biconjugate gradient and biconjugate gradient squared methods in Sonneveld. GMRES is presented by Saad and Schultz.

Conventions

The following conventions are used throughout this documentation:

`command`		This fixed-space font denotes literal items, such as pathnames, man page names, commands, and programming language structures.
`variable`		Italic typeface denotes variable entries and words or concepts being defined.
[ ]		Brackets enclose optional portions of a command line.

Obtaining Publications

You can obtain SGI documentation as follows:

See the SGI Technical Publications Library at http://docs.sgi.com. Various formats are available. This library contains the most recent and most comprehensive set of online books, release notes, man pages, and other information.
If it is installed on your SGI system, you can use InfoSearch, an online tool that provides a more limited set of online books, release notes, and man pages. With an IRIX system, enter infosearch at a command line or select Help -> InfoSearch from the Toolchest.
On IRIX systems, you can view release notes by entering either grelnotes or relnotes at a command line.
On Linux systems, you can view release notes on your system by accessing the README.txt file for the product. This is usually located in the /usr/share/doc/productname directory, although file locations may vary.
You can view man pages by typing man title at a command line.

Reader Comments

If you have comments about the technical accuracy, content, or organization of this publication, contact SGI. Be sure to include the title and document number of the publication with your comments. (Online, the document number is located in the front matter of the publication. In printed publications, the document number is located at the bottom of each page.)

You can contact SGI in any of the following ways:

Send e-mail to the following address:

techpubs@sgi.com
Use the Feedback option on the Technical Publications Library Web page:

http://docs.sgi.com
Contact your customer service representative and ask that an incident be filed in the SGI incident tracking system.
Send mail to the following address:
Technical Publications
SGI
1500 Crittenden Lane, M/S 535
Mountain View, California 94043-1351

SGI values your comments and will respond to them promptly.

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Scientific Computing Software Library (SCSL) User's Guide		Chapter 1. Introduction

SCSL User's Guide
(document number: 007-4325-001 / published: 2003-12-30)    table of contents  |  additional info  |  download

    Front Matter
    About This Guide
    Chapter 1. Introduction
    Chapter 2. Basic Linear Algebra Subprogram (BLAS) Routines
    Chapter 3. LAPACK
    Chapter 4. Using Sparse Linear Equation Solvers
    Chapter 5. Signal Processing Routines
    Appendix A. Supported SCSL Routines
    Glossary
    Index

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