Refining and verifying the solution of a linear system

Hong Diep Nguyen 1 Nathalie Revol 1
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : The problem considered here is to refine an approximate, numerical, solution of a linear system and simultaneously give 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. A new algorithm is given, which has been designed with these desirable properties in mind. It is based on iterative refinement for accuracy, with well-chosen computing precisions, and uses interval arithmetic for verification.
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Submitted on : Wednesday, November 16, 2011 - 1:47:16 PM
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Hong Diep Nguyen, Nathalie Revol. Refining and verifying the solution of a linear system. SNC 2011 - Symbolic Numeric Computation, Jun 2011, San Jose, United States. ⟨hal-00641659⟩

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