《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.

《数值算法的精确性与稳定性(第2版)》由汉安所著。

《数值算法的精确性与稳定性(第2版)》内容如下：

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. An expanded treatment of Gaussian elimination incorporates rook pivoting and additional error bounds. Other new toics include 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.

List of Figures

List of Tables

Preface to Second Edition

Preface to First Edition

About the Dedication

1 Principles of Finite Precision Computation

2 Floating Point Arithmetic

3 Basics

4 Summation

5 Polynomials

6 Norms

7 Perturbation Theory for Linear Systems

8 Triangular Systems

9 LU Factorization and Linear Equations

10 Cholesky Factorization

11 Symmetric Indefinite and Skew-Symmetric Systems

12 Iterative Refinement

13 Block LU Factorization

14 Matrix Inversion

15 Condition Number Estimation

16 The Sylvester Equation

17 Stationary Iterative Methods

18 Matrix Powers

19 QR Factorization

20 The Least Squares Problem

21 Underdetermined Systems

22 Vandermonde Svstems

23 Fast Matrix Multiplication

24 The Fast Fourier Transform and Applications

25 Nonlinear Systems and Newton's Method

26 Automatic Error Analysis

27 Software Issues in Floating Point Arithmetic

28 A Gallery of Test Matrices

A Solutions to Problems

B Acquiring Software

C Program Libraries

D The Matrix Computation Toolbox

Name Index

Subject Index