From the Publisher: 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 deve...
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ISBN:
(数字)9780898718027
ISBN:
(纸本)9780898715217
From the Publisher: 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. Historical perspective and insight are given, with particular reference to the fundamental work of Wilkinson and Turing, and 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 minimized, so that attention can be concentrated on accuracy and stability results. Here, in one place and in a unified notation, is error analysis for most of the standard algorithms.in matrix computations. 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. Although not designed specifically as a textbook, this volume is a suitable reference for an
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