Accuracy And Stability Of Numerical Algorithms

What is the most accurate way to sum floating point numbers? What are the advantages of IEEE arithmetic? How accurate is Gaussian elimination and what were the key breakthroughs in the development of error analysis for the method? The answers to these and many related questions are included here. This book gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis. Software practicalities are emphasized throughout, with particular reference to LAPACK and MATLAB. The best available error bounds, some of them new, are presented in a unified format with a minimum of jargon. Because of its central role in revealing problem sensitivity and providing error bounds, perturbation theory is treated in detail.