Hermann, Martin Numerical mathematics. 3rd revised and expanded ed. (Numerische Mathematik.) (German) Zbl 1254.65001 München: Oldenbourg Verlag (ISBN 978-3-486-70820-2/hbk; 978-3-486-71970-3/ebook). xiv, 563 p. (2011). For the intents and contents of the second edition see the previous review (2006; Zbl 1108.65001). In comparison this third edition has been revised and extended. To the chapter on numerical treatment of systems of nonlinear equations, a section on nonlinear fitting problems is added. In the center, there are the Gauss-Newton method, general methods of descent, the trust-region strategy and the Levenberg-Marquardt method. More MATLAB programs are taken into the text and codes already present are revised again. Reviewer: Rudolf Gorenflo (Berlin) Cited in 2 ReviewsCited in 1 Document MSC: 65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis 65Dxx Numerical approximation and computational geometry (primarily algorithms) 65Fxx Numerical linear algebra 65Hxx Nonlinear algebraic or transcendental equations 65G50 Roundoff error 65Txx Numerical methods in Fourier analysis 65Y15 Packaged methods for numerical algorithms 68W30 Symbolic computation and algebraic computation Keywords:error analysis; systems of linear and nonlinear equations; iterative methods; eigenvalue problems; interpolation; splines; numerical differentiation and integration; least squares; textbook; singular value decomposition; trigonometric interpolation; MATLAB routines; overdetermined systems; fast Givens transformations; fast Fourier transform Software:Matlab PDF BibTeX XML Cite \textit{M. Hermann}, Numerische Mathematik. 3rd revised and expanded ed. München: Oldenbourg Verlag (2011; Zbl 1254.65001)