Verified Numerical Linear Algebra: Linear System Solving

International audienceSolving 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