Rounding. 2. Precision. 3. Accuracy. 4. Higher Precision. 5. Tiny Relative Errors. University of Manchester. Nick Higham. Accuracy and Stability. Nick J Higham – School of Mathematics and Manchester Institute for Mathematical Sciences, The University of Manchester, UK. This book gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations.
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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 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.
An expanded treatment of Gaussian elimination incorporates rook pivoting, along with a thorough discussion of the choice of pivoting strategy and the effects of scaling.
The book’s detailed descriptions of floating point arithmetic and of software issues reflect the fact that IEEE arithmetic is now ubiquitous. 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.
With its thorough indexes and extensive, up-to-date bibliography, the book provides a mine of information in a readily accessible form.
Accuracy and Stability of Numerical Algorithms: Second Edition – Nicholas J. Higham – Google Books
From reviews of the first edition: Hitotumatu, Mathematical Reviews, Issue 97a. It covers 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.
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 odd hundred page sequel. But if not, he has more than earned his respite—and our gratitude. Principles of Finite Precision Computation; Chapter 2: Floating Point Arithmetic; Chapter 3: Perturbation Theory for Linear Systems; Chapter 8: Triangular Systems; Chapter 9: Cholesky Factorization; Chapter Iterative Refinement; Chapter Block LU Factorization; Chapter Matrix Inversion; Chapter Condition Number Estimation; Chapter The Sylvester Equation; Chapter Stationary Iterative Methods; Chapter Matrix Powers; Chapter QR Factorization; Chapter The Least Squares Problem; Chapter Underdetermined Systems; Chapter Vandermonde Systems; Chapter Fast Matrix Multiplication; Chapter Automatic Error Analysis; Chapter Solutions to Problems; Appendix B: Acquiring Software; Appendix C: Program Libraries; Appendix D: We promise to never spam you, and just use your email address to identify you as a valid customer.
Nick Higham – Accuracy and Stability of Numerical Algorithms
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