数值算法的精确性与稳定性

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

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 systems

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

bibliography

name index

subject index

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.