Minimizing convex quadratics with variable precision Krylov methods

Serge Gratton; Ehouarn Simon; Philippe Toint

Minimizing convex quadratics with variable precision Krylov methods

Serge Gratton, Ehouarn Simon, Philippe Toint

Namur Institute for Complex Systems

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Résumé

Iterative algorithms for the solution of convex quadratic optimization problems are investigated, which exploit inaccurate matrix-vector products. Theoretical bounds on the performance of a Conjugate Gradients and a Full-Orthormalization methods are derived, the necessary quantities occurring in the theoretical bounds estimated and new practical algorithms derived. Numerical experiments suggest that the new methods have significant potential, including in the steadily more important context of multi-precision computations.

langue originale	Anglais
Pages (de - à)	e2337
Nombre de pages	26
journal	Numerical Linear Algebra with Applications
Volume	28
Numéro de publication	1
Etat de la publication	Publié - 1 oct. 2020

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2 Article

A note on solving nonlinear optimization problems in variable precision
Gratton, S. & Toint, P. L., 1 juil. 2020, Dans: Computational Optimization and Applications. 76, 3, p. 917-933 17 p.
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Range-space variants and inexact matrix-vector products in Krylov solvers for linear systems arising from inverse problems
Gratton, S., Toint, P. & Tshimanga Ilunga, J., 1 janv. 2011, Dans: SIAM Journal on Matrix Analysis and Applications. 32, 3, p. 969-986 18 p.
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Minimizing convex quadratics with variable precision Krylov methods
Philippe Toint (Orateur)
28 nov. 2019
Activité: Discours ou présentation › Discours invité
ENSEEIHT-IRIT
Philippe Toint (Chercheur visiteur)
4 nov. 2019 → 8 nov. 2019
Activité: Visite d'une organisation externe › Visite à une institution académique externe
Minimizing convex quadratics with variable precision Krylov methods
Philippe Toint (Orateur)
10 oct. 2019
Activité: Discours ou présentation › Discours invité

Contient cette citation

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title = "Minimizing convex quadratics with variable precision Krylov methods",

abstract = "Iterative algorithms for the solution of convex quadratic optimization problems are investigated, which exploit inaccurate matrix-vector products. Theoretical bounds on the performance of a Conjugate Gradients and a Full-Orthormalization methods are derived, the necessary quantities occurring in the theoretical bounds estimated and new practical algorithms derived. Numerical experiments suggest that the new methods have significant potential, including in the steadily more important context of multi-precision computations.",

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AB - Iterative algorithms for the solution of convex quadratic optimization problems are investigated, which exploit inaccurate matrix-vector products. Theoretical bounds on the performance of a Conjugate Gradients and a Full-Orthormalization methods are derived, the necessary quantities occurring in the theoretical bounds estimated and new practical algorithms derived. Numerical experiments suggest that the new methods have significant potential, including in the steadily more important context of multi-precision computations.

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KW - multi-precision computing

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Minimizing convex quadratics with variable precision Krylov methods

Résumé

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Empreinte digitale

Résultat de recherche

A note on solving nonlinear optimization problems in variable precision

Range-space variants and inexact matrix-vector products in Krylov solvers for linear systems arising from inverse problems

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