research-article

Algorithm 937: MINRES-QLP for symmetric and Hermitian linear equations and least-squares problems

Authors:

Sou-Cheng T. Choi,

Michael A. SaundersAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 40, Issue 2

Article No.: 16, Pages 1 - 12

https://doi.org/10.1145/2527267

Published: 05 March 2014 Publication History

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.

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Software for MINRES-QLP for symmetric and Hermitian linear equations and least-squares problems

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References

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Index Terms

Algorithm 937: MINRES-QLP for symmetric and Hermitian linear equations and least-squares problems
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 40, Issue 2

February 2014

161 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2594412

Issue’s Table of Contents

Copyright © 2014 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Association for Computing Machinery

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Publication History

Published: 05 March 2014

Accepted: 01 September 2013

Revised: 01 September 2012

Received: 01 August 2011

Published in TOMS Volume 40, Issue 2

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https://doi.org/10.1088/2058-9565/ad7168
Wu FHe QLi YHan BWang Y(2024)Truncated Newton full waveform inversion method for the human brain imagingJournal of Physics: Conference Series10.1088/1742-6596/2822/1/0120132822:1(012013)Online publication date: 1-Sep-2024
https://doi.org/10.1088/1742-6596/2822/1/012013
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https://doi.org/10.21468/SciPostPhys.14.5.121
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