Algorithm 937

Abstract

We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite preconditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program units. In particular, we circumvent the need for reverse communication. Example test programs input and solve real or complex problems specified in Matrix Market format. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP.

Document Details

Document Type
Pub Defense Publication
Publication Date
Feb 01, 2014
Source ID
10.1145/2527267

Entities

People

  • Michael Saunders
  • Sou-cheng T. Choi

Organizations

  • National Science Foundation
  • Office of Advanced Scientific Computing Research
  • Office of Naval Research
  • Office of Science
  • Stanford University
  • United States Army Research Laboratory
  • United States Department of Energy
  • University of Chicago

Tags

Readers

  • Computer Science.
  • Linear Algebra
  • Systems Analysis and Design