Theoretical Numerical Analysis
Published on 12. May 2014
252 pages
978-1-4832-7522-2 (ISBN)
Description
Theoretical Numerical Analysis focuses on the presentation of numerical analysis as a legitimate branch of mathematics. The publication first elaborates on interpolation and quadrature and approximation. Discussions focus on the degree of approximation by polynomials, Chebyshev approximation, orthogonal polynomials and Gaussian quadrature, approximation by interpolation, nonanalytic interpolation and associated quadrature, and Hermite interpolation. The text then ponders on ordinary differential equations and solutions of equations. Topics include iterative methods for nonlinear systems, matrix eigenvalue problems, matrix inversion by triangular decomposition, homogeneous boundary value problems, and initial value problems. The publication takes a look at partial differential equations, including heat equation, stability, maximum principle, and first order systems. The manuscript is a vital source of data for mathematicians and researchers interested in theoretical numerical analysis.
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Content
PrefacePreliminariesChapter 1. Interpolation and Quadrature 1.1. Hermite Interpolation 1.2. Lagrange Interpolation and Newton-Cotes Quadrature 1.3. Orthogonal Polynomials and Gaussian Quadrature 1.4. Nonanalytic Interpolation and Associated Quadrature Exercises Computer Problems NotesChapter 2. Approximation 2.1. Degree of Approximation by Polynomials 2.2. Approximation by Interpolation 2.3. Chebyshev Approximation 2.4. An Algorithm for Chebyshev Approximation Appendix Exercises Computer Problems NotesChapter 3. Ordinary Differential Equations 3.1. The Initial Value Problem 3.2. An Inhomogeneous Boundary Value Problem 3.3. A Homogeneous Boundary Value Problem Exercises Computer Problems NotesChapter 4. Solution of Equations 4.1. Matrix Inversion by Triangular Decomposition 4.2. The Matrix Eigenvalue Problem 4.3. Linear Iterative Methods 4.4. Iterative Methods for Nonlinear Systems Exercises Computer Problem NotesChapter 5. Partial Differential Equations 5.1. First Order Systems 5.2. The Heat Equation 5.3. Stability 5.4. The Maximum Principle Exercises NotesReferencesAdditional ReadingAuthor IndexSubject Index
