Preconditioner Package

Software for Automatically Preconditioning the Conjugate Gradient Method

PREQN is a package of Fortran 77 subroutines for automatically generating preconditioners for the conjugate gradient method. It is designed for solving a sequence of linear systems A_i x=b_i, i=1,...,t, where the coefficient matrices A_i are symmetric and positive definite and vary slowly. The preconditioners are based on limited memory quasi-Newton updating and are recommended for problems in which: i) the coefficient matrices are not explicitly known and only matrix-vector products of the form A_i v can be computed; or ii) the coefficient matrices are not sparse. PREQN is written so that a single call from a conjugate gradient routine performs the preconditioning operation and stores information needed for the generation of a new preconditioner.

The current release is version 1.1. The distribution file was last changed on 01/01/2011.

Downloading and Installing the Preconditioner Package

Condition for Use: This software is freely available, but we expect that all publications describing work using this software quote at least one of the references given below.

You are welcome to grab the full Unix distribution, containing source code, makefile, and user guide.

CLICK HERE TO DOWNLOAD THE PRECONDITIONER PACKAGE DISTRIBUTION FILE

Save the gz file in a fresh subdirectory on your system. To install, first type

gunzip preqn.1.1.tar.gz

to produce a file preqn.1.1.tar. Then, type

tar -xvf preqn.1.1.tar

to have the source code, makefile and user guide put in the current directory.

Authors

Jose Luis Morales, Jorge Nocedal.

References

J.L. Morales and J. Nocedal, Automatic Preconditioning by Limited Memory Quasi-Newton Updating SIAM Journal on Optimization, 10, 4,pp. 1079-1096 (2000).
J.L. Morales and J. Nocedal, Algorithm PREQN: FORTRAN Subroutines for Preconditioning the Conjugate Gradient Method ACM Transactions on Mathematical Software, 27, 1, pp 83-91 (2001).