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 iAnccuracy and Stability of Numerical  Algorithms.This book gives a thorough 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, and pertubation theory is treated in detail. Historical perspective and insight are given, with particular reference to the fundamental work of Wilkinson and Turing. The many quotations provide further information  in an accessible format.The book is unique in that algorithmic developments and motivations are given succinctly and implementation details are minimized so that readers can concentrate on  accuracy and stability results. Not since Wilkinson’s Rounding Errors in Algebraic Processes(1963) and The Algebraic Eigenvalue Problem(1965) has any volume treated this   subject in such depth. A number of topics are treated that are not usually covered in numerical analysis textbooks, including floating point summation, block LU factorization, condition number estimation, the Sylvester equation, powers of matrices, finite precision behavior of stationary iterative methods, Vandermonde systems,   and fast matrix multiplication.