Accuracy and stability of numerical algorithms

摘要: From the Publisher: What is most accurate way to sum floating point numbers? What are advantages of IEEE arithmetic? How Gaussian elimination and what were key breakthroughs in development error analysis for method? The answers these many related questions included here. This book gives a thorough, up-to-date treatment behavior numerical algorithms finite precision arithmetic. It combines algorithmic derivations, perturbation theory, rounding analysis. Software practicalities emphasized throughout, with particular reference LAPACK MATLAB. best available bounds, some them new, presented unified format minimum jargon. Because its central role revealing problem sensitivity providing theory treated detail. Historical perspective insight given, fundamental work Wilkinson Turing, quotations provide further information an accessible format. The unique that developments motivations given succinctly implementation details minimized, so attention can be concentrated on accuracy stability results. Here, one place notation, standard matrix computations. Not since Wilkinson's Rounding Errors Algebraic Processes (1963) Eigenvalue Problem (1965) has any volume this subject such depth. A number topics not usually covered textbooks, including summation, block LU factorization, condition estimation, Sylvester equation, powers matrices, stationary iterative methods, Vandermonde systems, fast multiplication. Although designed specifically as textbook, suitable advanced course, could used by instructors at all levels supplementary text from which draw examples, historical perspective, statements results, exercises (many have never before appeared textbooks). comprehensive bibliography contains more than 1100 references research literature. Audience Specialists well computational scientists engineers concerned about their results will benefit book. Much understood only basic grounding linear algebra. About Author Nicholas J. Higham Professor Applied Mathematics University Manchester, England. He author 40 publications member editorial boards SIAM Journal Matrix Analysis Applications IMA Numerical Analysis. His Handbook Writing Mathematical Sciences was published 1993.