Numerical Methods Based on Sinc and Analytic Functions
Many mathematicians, scientists, and engineers are familiar with the Fast Fourier Transform, a method based upon the Discrete Fourier Transform. Perhaps not so many mathematicians, scientists, and engineers recognize that the Discrete Fourier Transform is one of a family of symbolic formulae called...
Main Author: | |
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Format: | eBook |
Language: | English |
Published: |
New York, NY
Springer New York
1993, 1993
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Edition: | 1st ed. 1993 |
Series: | Springer Series in Computational Mathematics
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Subjects: | |
Online Access: | |
Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 3.1 Sinc Approximation in Dd
- Problems for Section 3.1
- 3.2 Sinc Quadrature on (??, ?)
- Problems for Section 3.2
- 3.3 Discrete Fourier Transforms on (??,?)
- Problems for Section 3.3
- 3.4 Cauchy-Like Transforms on (??,?)
- Problems for Section 3.4
- 3.5 Approximation of Derivatives in Dd
- Problems for Section 3.5
- 3.6 The Indefinite Integral on (??, ?)
- Problems for Section 3.6
- Historical Remarks on Chapter 3
- 4 Sinc Approximation on ?
- 4.1 Basic Definitions
- Problems for Section 4.1
- 4.2 Interpolation and Quadrature on ?
- Problems for Section 4.2
- 4.3 Hilbert and Related Transforms on ?
- Problems for Section 4.3
- 4.4 Approximation of Derivatives on ?
- Problems for Section 4.4
- 4.5 Indefinite Integral Over ?
- Problems for Section 4.5
- 4.6 Indefinite Convolution Over ?
- Problemsfor Section 4.6
- Historical Remarks on Chapter 4
- 5 Sinc-Related Methods
- 5.1 Introduction
- 5.2 Variations of the Sinc Basis
- Problems for Section 5.2
- Problems for Section 6.9
- Historical Remarks on Chapter 6
- 7 Differential Equations
- 7.1 ODE-IVP
- Problems for Section 7.1
- 7.2 ODE-BVP
- Problems for Section 7.2
- 7.3 Analytic Solutions of PDE
- Problems for Section 7.3
- 7.4 Elliptic Problems
- Problems for Section 7.4
- 7.5 Hyperbolic Problems
- Problems for Section 7.5
- 7.6 Parabolic Problems
- Problems for Section 7.6
- Historical Remarks on Chapter 7
- References
- 1 Mathematical Preliminaries
- 1.1 Properties of Analytic Functions
- Problems for Section 1.1
- 1.2 Hilbert Transforms
- Problems for Section 1.2
- 1.3 Riemann—Hilbert Problems
- Problems for Section 1.3
- 1.4 Fourier Transforms
- Problems for Section 1.4
- 1.5 Laplace Transforms
- Problems for Section 1.5
- 1.6 Fourier Series
- Problems for Section 1.6
- 1.7 Transformations of Functions
- Problems for Section 1.7
- 1.8 Spaces of Analytic Functions
- Problems for Section 1.8
- 1.9 The Paley—Wiener Theorem
- Problems for Section 1.9
- 1.10 The Cardinal Function
- Problems for Section 1.10
- Historical Remarks on Chapter 1
- 2 Polynomial Approximation
- 2.1 Chebyshev Polynomials
- Problems for Section 2.1
- 2.2 Discrete Fourier Polynomials
- Problems for Section 2.2
- 2.3 The Lagrange Polynomial
- Problems for Section 2.3
- 2.4 Faber Polynomials
- Problems for Section 2.4
- Historical Remarks on Chapter 2
- 3 Sinc Approximation in Strip
- 5.3 Elliptic Function Interpolants
- Problems for Section 5.3
- 5.4 Inversion of the Laplace Transform
- Problems for Section 5.4
- 5.5 Sinc-Like Rational Approximation
- Problems for Section 5.5
- 5.6 Rationals and Extrapolation
- Problems for Section 5.6
- 5.7 Heaviside and Filter Rationals
- Problems for Section 5.7
- 5.8 Positive Base Approximation
- Problems for Section 5.8
- Historical Remarks on Chapter 5
- 6 Integral Equations
- 6.1 Introduction
- 6.2 Mathematical Preliminaries
- Problems for Section 6.2
- 6.3 Reduction to Algebraic Equations
- Problems for Section 6.3
- 6.4 Volterra Integral Equations
- Problems for Section 6.4
- 6.5 Potential Theory Problems
- Problems for Section 6.5
- 6.6 Reduced Wave Equation on a Half-Space
- Problems for Section 6.6
- 6.7 Cauchy Singular Integral Equations
- Problems for Section 6.7
- 6.8 Convolution-Type Equations
- Problems for Section 6.8
- 6.9 The Laplace Transform and Its Inversion