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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...

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Bibliographic Details
Main Author: Stenger, Frank
Format: eBook
Language:English
Published: New York, NY Springer New York 1993, 1993
Edition:1st ed. 1993
Series:Springer Series in Computational Mathematics
Subjects:
Numerical Analysis
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

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