This extremely popular textbook on numerical analysis provides the mathematical foundations of numerical methods. It demonstrates their performance on examples, exercises and real-life applications. This is done using the MATLAB software environment, which allows an easy implementation and testing of the algorithms for any specific class of problems. In this second edition, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been added. The book is addressed to students in Engineering, Mathematics, Physics and Computer Sciences. The attention to applications and software development makes it valuable also for users in a wide variety of professional fields.

Autorentext

Alfio Quarteroni (see http://www.cirs-tm.org/researchers/researchers.php?id=319): Author of a huge amount of books Professor and Chair of Modelling and Scientific Computing (CMCS) at the Institute of Analysis and Scientific Computing of EPFL, Lausanne (Switzerland), since 1998. Professor of Numerical Analysis at the Politecnico di Milano (Italy) since 1989 and Scientific Director of MOX, since 2002. Research Interests : His current research involves computational fluid dynamics, modelling and simulation of haemodynamics, numerical analysis of domain decomposition methods with application to multi-physics problems. Awards and Honors : NASA Group Achievement Award for the pioneering work in Computational Fluid Dynamics as a member of the ICASE numerical analysis and algorithms group, 1992. Member of the Lombard Academy of Science (Istituto Lombardo di Scienze e Lettere) (since 1995). Chairman of the Mathematics and Computer Science RTN evaluation panel of the E.U., 1999. Co-chairman (with P.L.Lions) of the AMIF research programme of the European Science Foundation (1996-2001). Recipient of the Galileian Chair, Scuola Normale Superiore, Pisa, Italy (2001). Premio Agrumello 2003. Laurea Honoris Causa in Naval Engineering , University of Trieste, Italy, October 2003. Recipient of one of the SIAM Outstanding Paper Prize 2004 (for a paper in collaboration with A. Veneziani and P. Zunino). IACM (International Association for Computational Mechanics), Fellow Award, 2004. Member of Accademia Nazionale dei Lincei, (Italian National Academy of Sciences) 2004. President of the Evaluation Panel "Mathematics and Computer Sciences" of CIVR, 2005.

Klappentext

This book provides the mathematical foundations of numerical methods and demonstrates their performance on examples, exercises and real-life applications. This is done using the MATLAB software environment, which allows an easy implementation and testing of the algorithms for any specific class of problems. The book is addressed to students in Engineering, Mathematics, Physics and Computer Sciences. In the second edition of this extremely popular textbook on numerical analysis, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been

Inhalt

Series Preface.- Preface.- I Getting Started.- 1. Foundations of Matrix Analysis.- 2 Principles of Numerical Mathematics.- II Numerical Linear Algebra.- 3 Direct Methods for the Solution of Linear Systems.- 4 Iterative Methods for Solving Linear Systems.- 5 Approximation of Eigenvalues and Eigenvectors.- III Around Functions and Functionals.- 6 Rootfinding for Nonlinear Equations.- 7 Nonlinear Systems and Numerical Optimization.- 8 Polynomial Interpolation.- 9 Numerical Integration.- IV Transforms, Differentiation and Problem Discretization.- 10 Orthogonal Polynomials in Approximation Theory.- 11 Numerical Solution of Ordinary Differential Equations.- 12 Two-Point Boundary Value Problems.- 13 Parabolic and Hyperbolic Initial Boundary Value Problems.- References.- Index of MATLAB Programs.- Index.