Elementary numerical analysis. An algorithmic approach. Updated with MATLAB. Reprint of the third edition 1980. (English) Zbl 1392.65002

Conte, S. D.; de Boor, Carl

Classics in Applied Mathematics 78. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-61197-519-2/pbk; 978-1-61197-520-8/ebook). xxiv, 456 p. (2018).

This is a reprint of the 3rd edition of this book of 1980 [Zbl 0496.65001]. The text has not been changed but there is a new preface where de Boor explains that he has added now MATLAB routines. He had proposed these for the 1980 edition but his co-author and the editor preferred to stick to the Fortran routines inserted in the text. These are still there but their MATLAB transcription has been added in an appendix. Since 1980 some typos and smaller flaws were discovered, which are added as a list with errata in the beginning of the book. So the original page numbers are not changed. The book is a textbook with exercises giving an introduction to numerical analysis. More recent textbooks may have shifted emphasis to different chapters and Fortran would probably not be the preferred code nowadays. But even though this book is written in 1980, the basics did not change fundamentally. That is why it is still of interest and fortunately SIAM is saving it from oblivion, by making it one of its Classics in Applied Mathematics, since the book has been out of print.
See the reviews of the first and second editions in [Zbl 0213.41501; Zbl 0257.65002].

Reviewer: Adhemar Bultheel (Leuven)

MSC:

65-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65G50	Roundoff error
65Dxx	Numerical approximation and computational geometry (primarily algorithms)
41A05	Interpolation in approximation theory
41A15	Spline approximation
41A55	Approximate quadratures
65Hxx	Nonlinear algebraic or transcendental equations
65F05	Direct numerical methods for linear systems and matrix inversion
65F10	Iterative numerical methods for linear systems
65F15	Numerical computation of eigenvalues and eigenvectors of matrices
65L05	Numerical methods for initial value problems
65L10	Numerical solution of boundary value problems involving ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations
65-04	Software, source code, etc. for problems pertaining to numerical analysis

Keywords:

unconstrained optimization; fast Fourier transform; adaptive quadrature; step size control; Runge-Kutta methods; stiff differential equations; exercises; textbook

Software:

dverk; EISPACK; IMSL Numerical Libraries; LINPACK; Matlab