Refining and verifying efficiently the solution of a linear system

International audienceThe 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