Formal Proofs of Rounding Error Bounds With Application to an Automatic Positive Definiteness Check

摘要

Floating-point arithmetic is a very efficient solution to perform computations in the real field. However, it induces rounding errors making results computed in floating-point differ from what would be computed with reals. Although numerical analysis gives tools to bound such differences, the proofs involved can be painful, hence error prone. We thus investigate the ability of a proof assistant like Coq to mechanically check such proofs. We demonstrate two different results involving matrices, which are pervasive among numerical algorithms, and show that a large part of the development effort can be shared between them.