《数值算法的精确性与稳定性(第2版)(影印版)》内容简介：accuracy and stability of numerical algorithms 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, all enlivened by historical perspective and informative quotations.
this second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and newton's method. twelve new sections include coverage of additional error bounds for gaussian elimination, rank revealing lu factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures. although not designed specifically as a textbook, this new edition is a suitable reference for an advanced course. it can also be used by instructors at all levels as a supplementary text from which to draw examples, historical perspective, statements of results, and exercises. 作者简介
Nicholas J. Higham is Richardson Professor of Applied Mathematics at the University of Manchester, England. He is the author of more than 80 publications and is a member of the editorial boards of Foundations of Computational Mathematics, the IMA Journal of Numerical Analysis, Linear Algebra and Its Applications, and the SIAM Journal on Matrix Analysis and Applications.
目录
List of FiguresList of TablesPreface to Second EditionPreface to First EditionAbout the Dedication1 Principles of Finite Precision Computation2 Floating Point Arithmetic3 Basics4 Summation5 Polynomials6 Norms7 Perturbation Theory for Linear Systems8 Triangular Systems9 LU Factorization and Linear Equations10 Cholesky Factorization11 Symmetric Indefinite and Skew-Symmetric Systems12 Iterative Refinement13 Block LU Factorization14 Matrix Inversion15 Condition Number Estimation16 The Sylvester Equation17 Stationary Iterative Methods18 Matrix Powers19 QR Factorization20 The Least Squares Problem21 Underdetermined Systems22 Vandermonde Svstems23 Fast Matrix Multiplication24 The Fast Fourier Transform and Applications25 Nonlinear Systems and Newton's Method26 Automatic Error Analysis27 Software Issues in Floating Point Arithmetic28 A Gallery of Test MatricesA Solutions to ProblemsB Acquiring SoftwareC Program LibrariesD The Matrix Computation ToolboxName IndexSubject Index
List of FiguresList of TablesPreface to Second EditionPreface to First EditionAbout the Dedication1 Principles of Finite Precision Computation2 Floating Point Arithmetic3 Basics4 Summation5 Polynomials6 Norms7 Perturbation Theory for Linear Systems8 Triangular Systems9 LU Factorization and Linear Equations10 Cholesky Factorization11 Symmetric Indefinite and Skew-Symmetric Systems12 Iterative Refinement13 Block LU Factorization14 Matrix Inversion15 Condition Number Estimation16 The Sylvester Equation17 Stationary Iterative Methods18 Matrix Powers19 QR Factorization20 The Least Squares Problem21 Underdetermined Systems22 Vandermonde Svstems23 Fast Matrix Multiplication24 The Fast Fourier Transform and Applications25 Nonlinear Systems and Newton's Method26 Automatic Error Analysis27 Software Issues in Floating Point Arithmetic28 A Gallery of Test MatricesA Solutions to ProblemsB Acquiring SoftwareC Program LibrariesD The Matrix Computation ToolboxName IndexSubject Index
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