Search results for "Gauss–Kronrod quadrature formula"
showing 5 items of 5 documents
Quadrature rules for qualocation
2003
Qualocation is a method for the numerical treatment of boundary integral equations on smooth curves which was developed by Chandler, Sloan and Wendland (1988-2000) [1,2]. They showed that the method needs symmetric J–point–quadrature rules on [0, 1] that are exact for a maximum number of 1–periodic functions The existence of 2–point–rules of that type was proven by Chandler and Sloan. For J ∈ {3, 4} such formulas have been calculated numerically in [2]. We show that the functions Gα form a Chebyshev–system on [0, 1/2] for arbitrary indices a and thus prove the existence of such quadrature rules for any J.
An analysis of Ralston's quadrature
1987
Ralston's quadrature achieves higher accuracy in composite rules than analogous Newton-Cotes or Gaussian formulas. His rules are analyzed, computable expressions for the weights and knots are given, and a more suitable form of the remainder is derived.
Rational Hermite Interpolation and Quadrature
1993
Rational Hermite interpolation is used in two different ways in order to derive and analyze quadrature rules. One approach yields quadratures of Gaussian-type whereas the other one generalizes Engels’ dual quadratures exhibiting the close connection between rational Hermite interpolation and quadrature in general.
Quadrature Formula Based on Interpolating Polynomials: Algorithmic and Computational Aspects
2007
The aim of this article is to obtain a quadrature formula for functions in several variables and to analyze the algorithmic and computational aspects of this formula. The known information about the integrand is {λi(f)}i=1n, where λi are linearly independent linear functionals. We find a form of the coefficients of the quadrature formula which can be easy used in numerical calculations. The main algorithm we use in order to obtain the coefficients and the remainder of the quadrature formula is based on the Gauss elimination by segments method. We obtain an expression for the exactness degree of the quadrature formula. Finally, we analyze some computational aspects of the algorithm in the pa…
Gaussian quadrature rule for arbitrary weight function and interval
2005
Abstract A program for calculating abscissas and weights of Gaussian quadrature rules for arbitrary weight functions and intervals is reported. The program is written in Mathematica. The only requirement is that the moments of the weight function can be evaluated analytically in Mathematica. The result is a FORTRAN subroutine ready to be utilized for quadrature. Program summary Title of program: AWGQ Catalogue identifier:ADVB Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVB Program obtained from: CPC Program Library, Queens University, Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Computers: Pentium IV 1.7 GHz processor Ins…