Numerical mathematics. (Matematica numerica). 2nd ed. (Matematica numerica.) (Italian) Zbl 0943.65001

Quarteroni, A.; Sacco, R.; Saleri, F.

Milano: Springer. xiv, 440 p. (2000).

[For a review of the first edition (1998) see Zbl 0913.65002.]
The aim of this book is to present in a systematic manner various numerical methods related to stability properties, accurateness and algorithmic complexity and to show, via examples and counterexamples, the advantages and the weak points of each method. This book is organized in the following 11 chapters:
1) Elements of matrix analysis.
2) Foundations of numerical mathematics.
3) Solution of linear systems with direct methods.
4) Solution of linear systems with iterative methods.
5) Approximation of eigenvalues and eigenvectors.
6) Solutions of nonlinear equations and systems.
7) Polynomial approximation of functions and data.
8) Numerical integration.
9) Orthogonal polynomial in approximation theory.
10) Numerical solution of ordinary differential equations.
11) Approximation of limit problems.
This book is addressed mainly to students in engineering, mathematics, computer science and physics. The students need the knowledge of calculus and linear algebra. This book is also useful to reasearchers in other fields needing computational techniques. The programs for many algorithms are also given in MATLAB.

Reviewer: R.S.Dahiya (Ames)

MSC:

65-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65Fxx	Numerical linear algebra
65Hxx	Nonlinear algebraic or transcendental equations
65Dxx	Numerical approximation and computational geometry (primarily algorithms)
65Lxx	Numerical methods for ordinary differential equations
65B05	Extrapolation to the limit, deferred corrections

Keywords:

textbook; polynomial approximation; numerical integration; orthogonal polynomial; stability; complexity; examples; counterexamples; matrix analysis; direct methods; iterative methods; eigenvalues; eigenvectors; nonlinear equations; systems; ordinary differential equations; programs; MATLAB

Software:

Matlab