Some a Posteriori Error Bounds in Floating Point Computations

摘要

By using consistently the a posteriori models for bounding round-off errors in the basic floating-point operations, the author has in the paper some useful a posteriori error bounds which can be computed without too expensive computing efforts. Forward error bounds are found for inner product and polynomial evaluations. The analysis of Crout algorithm in solving systems of linear algebriac equations leads to some useful backward a posteriori bounds which are sharper than the corresponding a priori ones given by Wilkinson. The results in the analysis of the iterative refinement procedure for solving systems of linear algebraic equations gives some useful bounds for estimating the rate of convergence of the procedure. Some numerical experiments are also included. (Author Modified Abstract)