Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Error bounds from extra-precise iterative refinement
ACM Transactions on Mathematical Software (TOMS)
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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.