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Über dieses Buch

Numerical mathematics proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations.

This book provides the mathematical foundations of numerical methods and demonstrate 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. The attention to applications and software development makes it valuable also for users in a wide variety of professional fields.

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.

Inhaltsverzeichnis

Frontmatter

Getting Started

2007 | OriginalPaper | Buchkapitel

1. Foundations of Matrix Analysis

Alfio Quarteroni, Riccardo Sacco, Fausto Saleri

2007 | OriginalPaper | Buchkapitel

2. Principles of Numerical Mathematics

Alfio Quarteroni, Riccardo Sacco, Fausto Saleri

Numerical Linear Algebra

2007 | OriginalPaper | Buchkapitel

3. Direct Methods for the Solution of Linear Systems

Alfio Quarteroni, Riccardo Sacco, Fausto Saleri

2007 | OriginalPaper | Buchkapitel

4. Iterative Methods for Solving Linear Systems

Alfio Quarteroni, Riccardo Sacco, Fausto Saleri

2007 | OriginalPaper | Buchkapitel

5. Approximation of Eigenvalues and Eigenvectors

Alfio Quarteroni, Riccardo Sacco, Fausto Saleri

Around Functions and Functionals

2007 | OriginalPaper | Buchkapitel

6. Rootfinding for Nonlinear Equations

Alfio Quarteroni, Riccardo Sacco, Fausto Saleri

2007 | OriginalPaper | Buchkapitel

7. Nonlinear Systems and Numerical Optimization

Alfio Quarteroni, Riccardo Sacco, Fausto Saleri

2007 | OriginalPaper | Buchkapitel

8. Polynomial Interpolation

Alfio Quarteroni, Riccardo Sacco, Fausto Saleri

2007 | OriginalPaper | Buchkapitel

9. Numerical Integration

Alfio Quarteroni, Riccardo Sacco, Fausto Saleri

Transforms, Differentiation and Problem Discretization

2007 | OriginalPaper | Buchkapitel

10. Orthogonal Polynomials in Approximation Theory

Alfio Quarteroni, Riccardo Sacco, Fausto Saleri

2007 | OriginalPaper | Buchkapitel

11. Numerical Solution of Ordinary Differential Equations

Alfio Quarteroni, Riccardo Sacco, Fausto Saleri

2007 | OriginalPaper | Buchkapitel

12. Two-Point Boundary Value Problems

Alfio Quarteroni, Riccardo Sacco, Fausto Saleri

2007 | OriginalPaper | Buchkapitel

13. Parabolic and Hyperbolic Initial Boundary Value Problems

Alfio Quarteroni, Riccardo Sacco, Fausto Saleri

Backmatter

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