Numerical mathematics. (Matematica numerica). 2nd ed.
(Matematica numerica.)

*(Italian)*Zbl 0943.65001
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.

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 |