Generalized Gaussian Quadrature Rules for Systems of Arbitrary Functions

Abstract

In an earlier work, a far-reaching generalization of the classical Gaussian quadrature rules is introduced, replacing the polynomials with a wide class of functions. While the rules of in that report possess most of the desirable properties of the classical Gaussian integration formulae (positivity of the weights, etc.), it is not clear from siad research how much quadrature rules can obtained numerically. In this paper, we present a numerical scheme for the generation of such generalized Gaussian quadratures. The algorithm is applicable to a variety of functions, including smooth functions as well as functions with end-point singularities. The performance of the algorithm is demonstrated with several numerical examples

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1993
Accession Number
ADA273610

Entities

People

  • Jianpeng Ma
  • S. Wandzura
  • Vladimir Rokhlin

Organizations

  • Yale University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Bessel Functions
  • Chebyshev Approximations
  • Chebyshev Polynomials
  • Coefficients
  • Construction
  • Differential Equations
  • Equations
  • Gaussian Quadrature
  • Integral Equations
  • Integrals
  • Intervals
  • Numbers
  • Partial Differential Equations
  • Polynomials
  • Real Numbers
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis