Exploiting variable precision in GMRES

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

Exploiting variable precision in GMRES

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

Namur Institute for Complex Systems

Research output: Working paper

24 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 language	English
Number of pages	19
Volume	1907:10550
Publication status	Published - Jul 2019

Keywords

numerical analysis
variable precision
Krylov methods
ilinear algebra

Access to Document

arXiv-1907.10550Submitted manuscript, 163 KB

1 Article

A note on solving nonlinear optimization problems in variable precision
Gratton, S. & Toint, P. L., 1 Jul 2020, In: Computational Optimization and Applications. 76, 3, p. 917-933 17 p.
Research output: Contribution to journal › Article › peer-review

Open Access
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2 Invited talk
1 Visiting an external academic institution

Minimizing convex quadratics with variable precision Krylov methods
Philippe Toint (Speaker)
28 Nov 2019
Activity: Talk or presentation types › Invited talk
ENSEEIHT-IRIT
Philippe Toint (Visiting researcher)
4 Nov 2019 → 8 Nov 2019
Activity: Visiting an external institution types › Visiting an external academic institution
Minimizing convex quadratics with variable precision Krylov methods
Philippe Toint (Speaker)
10 Oct 2019
Activity: Talk or presentation types › Invited talk

Cite this

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title = "Exploiting variable precision in GMRES",

abstract = "We describe how variable precision floating point arithmetic can be used inthe iterative solver GMRES. We show how the precision of the inner productscarried out in the algorithm can be reduced as the iterations proceed, withoutaffecting the convergence rate or final accuracy achieved by the iterates.Our analysis explicitly takes into account the resulting loss of orthogonalityin the Arnoldi vectors. We also show how inexact matrix-vector products canbe incorporated into this setting.",

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AU - Titley-Peloquin, David

AU - Toint, Philippe

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N2 - We describe how variable precision floating point arithmetic can be used inthe iterative solver GMRES. We show how the precision of the inner productscarried out in the algorithm can be reduced as the iterations proceed, withoutaffecting the convergence rate or final accuracy achieved by the iterates.Our analysis explicitly takes into account the resulting loss of orthogonalityin the Arnoldi vectors. We also show how inexact matrix-vector products canbe incorporated into this setting.

AB - We describe how variable precision floating point arithmetic can be used inthe iterative solver GMRES. We show how the precision of the inner productscarried out in the algorithm can be reduced as the iterations proceed, withoutaffecting the convergence rate or final accuracy achieved by the iterates.Our analysis explicitly takes into account the resulting loss of orthogonalityin the Arnoldi vectors. We also show how inexact matrix-vector products canbe incorporated into this setting.

KW - numerical analysis

KW - variable precision

KW - Krylov methods

KW - ilinear algebra

M3 - Working paper

VL - 1907:10550

BT - Exploiting variable precision in GMRES

ER -

Exploiting variable precision in GMRES

Abstract

Keywords

Access to Document

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Research output

A note on solving nonlinear optimization problems in variable precision

Activities

Minimizing convex quadratics with variable precision Krylov methods

ENSEEIHT-IRIT

Minimizing convex quadratics with variable precision Krylov methods

Cite this