Handbook of computational methods for integration. (©2005)

• Record Type: Book
• Further Information: Note: Prem K. Kythe, Michael R. Schäferkotter.
• Other Names: Kythe, Prem K; Schäferkotter, Michael R, 1955-
• Contents: Preface ; Notation ; Preliminaries ; Notation and Definitions; Orthogonal Polynomials; Finite and Divided Differences; Interpolation; Semi-Infinite Interval; Convergence Accelerators; Polynomial Splines; Interpolatory Quadrature ; Riemann Integration; Euler-Maclaurin Expansion; Interpolatory Quadrature Rules; Newton-Cotes Formulas; Basic Quadrature Rules; Repeated Quadrature Rules; Romberg’s Scheme; Gregory’s Correction Scheme; Interpolatory Product Integration; Iterative and Adaptive Schemes; Test Integrals; Gaussian Quadrature ; Gaussian Rules; Extended Gaussian Rules; Other Extended Rules; Analytic Functions; Bessel’s Rule; Gaussian Rules for the Moments; Finite Oscillatory Integrals; Noninterpolatory Product Integration; Test Integrals; Improper Integrals ; Infinite Range Integrals; Improper Integrals ; Slowly Convergent Integrals; Oscillatory Integrals; Product Integration; Singular Integrals ; Quadrature Rules; Product Integration; Acceleration Methods; Singular and Hypersingular Integrals; Computer-Aided Derivations; Fourier Integrals and Transforms ; Fourier Transforms; Interpolatory Rules for Fourier Integrals; Interpolatory Rules by Rational Functions; Trigonometric Integrals; Finite Fourier Transforms; Discrete Fourier Transforms; Hartley Transform; Inversion of Laplace Transforms ; Use of Orthogonal Polynomials; Interpolatory Methods; Use of Gaussian Quadrature Rules; Use of Fourier Series; Use of Bromwich Contours; Inversion by the Riemann Sum; New Exact Laplace Inverse Transforms; Wavelets ; Orthogonal Systems; Trigonometric System; Haar System; Other Wavelet Systems; Daubechies’ System; Fast Daubechies Transforms ; Integral Equations ; Nyström System; Integral Equations of the First Kind; Integral Equations of the Second Kind; Singular Integral Equations; Weakly Singular Equations; Cauchy Singular Equations of the First Kind; Cauchy Singular Equations of the Second Kind; Canonical Equation; Finite-Part Singular Equations; Integral Equations Over a Contour; Appendix A: Quadrature Tables ; Cotesian Numbers, Tabulated for k£n/2, n=1(1)11; Weights for a Single Trapezoidal Rule and Repeated Simpson’s Rule; Weights for Repeated Simpson’s Rule and a Single Trapezoidal Rule; Weights for a Single 3/8-Rule and Repeated Simpson’s Rule; Weights for Repeated Simpson’s Rule and a Single 3/8-Rule; Gauss-Legendre Quadrature; Gauss-Laguerre Quadrature; Gauss-Hermite Quadrature; Gauss-Radau Quadrature; Gauss-Lobatto Quadrature; Nodes of Equal-Weight Chebyshev Rule; Gauss-Log Quadrature; Gauss-Kronrod Quadrature Rule; Patterson’s Quadrature Rule; Filon’s Quadrature Formula; Gauss-Cos Quadrature on [π/2, π/2]; Gauss-Cos Quadrature on [0, π/2]; Coefficients in (5.1.15) with w(x)=ln(1/x), 0
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2005
• Copyright Date: 2005
• Extent: 1 online resource (xxii, 598 pages), illustrations
• Subjects: 518/.54; Numerical integration; Integrals; Orthogonal polynomials; MATHEMATICS -- Numerical Analysis; Integrals; Numerical integration; Orthogonal polynomials; Electronic books
• Languages: English
• ISBNs: 0203490304; 9780203490303; 9781584884286; 1584884282
• Related ISBNs: 1584884282
• Notes: Note: Includes bibliographical references (pages 551-583) and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.