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Verified Numerical Linear Algebra: Linear System Solving

Nathalie Revol 1 
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Solving numerically a linear system can be performed very efficiently, using optimized routines, but it yields an approximate solution without any indication about its accuracy. Getting an enclosure of the error between the approximate and the exact solutions is called "verification". We present a verified algorithm which gets an accurate enclosure, with a moderate overhead both in complexity and in practical performance. Its key ingredients are interval arithmetic, iterative refinement and well-chosen computing precision.
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Submitted on : Wednesday, November 16, 2011 - 1:53:52 PM
Last modification on : Tuesday, October 25, 2022 - 4:22:48 PM


  • HAL Id : hal-00641663, version 1


Nathalie Revol. Verified Numerical Linear Algebra: Linear System Solving. 2011 SIAM Conference on Applied Algebraic Geometry, Oct 2011, Raleigh, United States. ⟨hal-00641663⟩



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