Numerical methods. Design, analysis, and computer implementation of algorithms.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1247.65001
author: Timothy P. Chartier
author: Anne Greenbaum
publication date: 2012-04-16T00:00:00Z
Mathematics Subject Classification ID: 65-01
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L10
zbMATH DE Number: 6024385
zbMATH Keywords: textbook
zbMATH Keywords: algorithms
zbMATH Keywords: nonlinear equations
zbMATH Keywords: linear systems
zbMATH Keywords: iterative methods
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: polynomial interpolation
zbMATH Keywords: mathematical modeling
zbMATH Keywords: Monte Carlo methods
zbMATH Keywords: numerical differentiation
zbMATH Keywords: numerical integration
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: initial value problem
zbMATH Keywords: boundary value problem
zbMATH Keywords: partial differential equations
zbMATH Keywords: MATLAB
zbMATH Keywords: least squares problem
zbMATH Keywords: Richardson extrapolation
describes a project that uses: SageMath
describes a project that uses: hfloat
describes a project that uses: Matlab
describes a project that uses: Chebfun
MaRDI profile type: Publication
title: Numerical methods. Design, analysis, and computer implementation of algorithms.
review text: This is a textbook on numerical methods that offers a modern and rigorous presentation, at a medium level of training in Mathematics. It provides a well balanced amount of theory and illustrative examples, supported by an attractive exposition style. The reader can find proofs of the important results, technical details relevant for applications, as well as interesting information about the historical background. The presentation of various algorithms is accompanied by MATLAB codes. Exercises are carefully selected and an electronic version of a Solutions Manual is available.NEWLINENEWLINEThe material is structured in 14 chapters and two appendices, as follows: 1. Mathematical modeling, 2. Basic operations with MATLAB, 3. Monte Carlo methods, 4. Solution of a single nonlinear equation in one unknown, 5. Floating-point arithmetic, 6. Conditioning of problems; stability of algorithms, 7. Direct methods for solving linear systems and least squares problems, 8. Polynomial and piecewise polynomial interpolation, 9. Numerical differentiation and Richardson extrapolation, 10. Numerical integration, 11. Numerical solution of the initial value problem for ordinary differential equations, 12. More numerical linear algebra, eigenvalues and iterative methods for solving linear systems, 13. Numerical solution of two-point boundary value problems, 14. Numerical solution of partial differential equations, Appendix A. Review of linear algebra, Appendix B. Taylor's theorem in multidimensions.NEWLINENEWLINEThe book is equally recommended to students motivated for a deeper individual work and educators interested in the development of effective teaching instruments (lecture notes, computer exercises etc.).
reviewed by: Octavian Pastravanu
description: scientific article; zbMATH DE number 6024385