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.
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. His book Handbook of Writing for the Mathematical Sciences (second edition) was published by SIAM in 1998, and his book MATLAB Guide, co-authored with Desmond J. Higham, was published by SIAM in 2000.
List of Figures List of Tables Preface to Second Edition Preface to First Edition About the Dedication Chapter 1: Principles of Finite Precision Computation Chapter 2: Floating Point Arithmetic Chapter 3: Basics Chapter 4: Summation Chapter 5: Polynomials Chapter 6: Norms Chapter 7: Perturbation Theory for Linear Systems Chapter 8: Triangular Systems Chapter 9: LU Factorization and Linear Equations Chapter 10: Cholesky Factorization Chapter 11: Symmetric Indefinite and Skew-Symmetric Systems Chapter 12: Iterative Refinement Chapter 13: Block LU Factorization Chapter 14: Matrix Inversion Chapter 15: Condition Number Estimation Chapter 16: The Sylvester Equation Chapter 17: Stationary Iterative Methods Chapter 18: Matrix Powers Chapter 19: QR Factorization Chapter 20: The Least Squares Problem Chapter 21: Underdetermined Systems Chapter 22: Vandermonde Systems Chapter 23: Fast Matrix Multiplication Chapter 24: The Fast Fourier Transform and Applications Chapter 25: Nonlinear Systems and Newton's Method Chapter 26: Automatic Error Analysis Chapter 27: Software Issues in Floating Point Arithmetic Chapter 28: A Gallery of Test Matrices Appendix A: Solutions to Problems Appendix B: Acquiring Software Appendix C: Program Libraries Appendix D: The Matrix Computation Toolbox Bibliography Name Index Subject Index
'This book is a monumental work on the analysis of rounding error and will serve as a new standard textbook on this subject, especially for linear computation.' S. Hitotumatu, Mathematical Reviews '...This definitive source on the accuracy and stability of numerical algorithms is quite a bargain and a worthwhile addition to the library of any statistician heavily involved in computing.' Robert L. Strawderman, Journal of the American Statistical Association '...A monumental book that should be on the bookshelf of anyone engaged in numerics, be it as a specialist or as a user.' A. van der Sluis, ITW Nieuws 'This text may become the new 'Bible' about accuracy and stability for the solution of systems of linear equations. It covers 688 pages carefully collected, investigated, and written ... One will find that this book is a very suitable and comprehensive reference for research in numerical linear algebra, software usage and development, and for numerical linear algebra courses.' N. Kockler, Zentrallblatt fur Mathematik '... Nick Higham has assembled an enormous amount of important and useful material in a coherent, readable form. His book belongs on the shelf of anyone who has more than a casual interest in rounding error and matrix computations. I hope the author will give us the 600-odd page sequel. But if not, he has more than earned his respite - and our gratitude.' G. W. Stewart, SIAM Review
