Activities per year
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.
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
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Activities
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)
28 Nov 2019
Activity: Talk or presentation types › Invited talk
Minimizing convex quadratics with variable precision Krylov methods
Philippe Toint (Speaker)
10 Oct 2019
Activity: Talk or presentation types › Invited talk
Cite this
Gratton, S., Simon, E., Titley-Peloquin, D., & Toint, P. (2019). Exploiting variable precision in GMRES.