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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.
Chapter 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
Chapter 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
Chapter 3. Ordinary Differential Equations
3.1. The Initial Value Problem
3.2. An Inhomogeneous Boundary Value Problem
3.3. A Homogeneous Boundary Value Problem
Chapter 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
Chapter 5. Partial Differential Equations
5.1. First Order Systems
5.2. The Heat Equation
5.4. The Maximum Principle
- No. of pages:
- © Academic Press 1966
- 1st January 1966
- Academic Press
- eBook ISBN:
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