Exploiting variable precision in GMRES

Serge Gratton, Ehouarn Simon, David Titley-Peloquin, Philippe Toint

Research output: Working paper

4 Downloads (Pure)

Abstract

We describe how variable precision floating point arithmetic can be used in
the iterative solver GMRES. We show how the precision of the inner products
carried out in the algorithm can be reduced as the iterations proceed, without
affecting the convergence rate or final accuracy achieved by the iterates.
Our analysis explicitly takes into account the resulting loss of orthogonality
in the Arnoldi vectors. We also show how inexact matrix-vector products can
be incorporated into this setting.
Original languageEnglish
Number of pages19
Volume1907:10550
Publication statusPublished - Jul 2019

Keywords

  • numerical analysis
  • variable precision
  • Krylov methods
  • ilinear algebra

Fingerprint Dive into the research topics of 'Exploiting variable precision in GMRES'. Together they form a unique fingerprint.

  • Activities

    • 2 Invited talk
    • 1 Visiting an external academic institution

    ENSEEIHT-IRIT

    Philippe Toint (Visiting researcher)

    4 Nov 20198 Nov 2019

    Activity: Visiting an external institution typesVisiting an external academic institution

    Minimizing convex quadratics with variable precision Krylov methods

    Philippe Toint (Speaker)

    28 Nov 2019

    Activity: Talk or presentation typesInvited talk

    Minimizing convex quadratics with variable precision Krylov methods

    Philippe Toint (Speaker)

    10 Oct 2019

    Activity: Talk or presentation typesInvited talk

    Cite this

    Gratton, S., Simon, E., Titley-Peloquin, D., & Toint, P. (2019). Exploiting variable precision in GMRES.