Refining and verifying efficiently the solution of a linear system

Nathalie Revol 1 Hong Diep Nguyen 1
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : The problem considered in this talk is to solve and mainly to refine an approximate, numerical, solution of a linear system. The refinement step is computed simultaneously with an enclosure of the error between this approximate solution and the exact one: this is the verification step. Desirable properties for an algorithm solving this problem are accuracy of the results, complexity and performance of the actual implementation. In this talk, an algorithm is presented, which aims at satisfying these properties. It is based on the use of BLAS3 optimized routines for performances. It employs iterative refinement for accuracy, with well-chosen computing precisions, and it uses interval arithmetic for verification.
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Conference papers
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https://hal.inria.fr/hal-00641669
Contributor : Nathalie Revol <>
Submitted on : Wednesday, November 16, 2011 - 2:02:02 PM
Last modification on : Thursday, January 17, 2019 - 3:16:03 PM

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Nathalie Revol, Hong Diep Nguyen. Refining and verifying efficiently the solution of a linear system. Dagstuhl Seminar 11371: Uncertainty modeling and analysis with intervals: Foundations, tools, applications, Sep 2011, Dagstuhl, Germany. ⟨hal-00641669⟩

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