Gaussian Quadrature Formulae for Arbitrary Positive Measures
نویسندگان
چکیده
منابع مشابه
Gaussian Quadrature Formulae for Arbitrary Positive Measures
We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known...
متن کاملOn Multiple Node Gaussian Quadrature Formulae
k Abstract. Let fip . . , Hk be odd positive integers and »i = Z¡=.x(p¡ + 1). Let {«(.}|=j be an extended Tchebycheff system on [a, b]. Let L be a positive linear functional on U = span( {u,}). We prove that L has a unique representation in the form k M,— 1 £<p) = E Z "i/PW(f,). « < h < ■ ■ • < tk < b, 1=1 ;=0 _ k for all p G U. The proof uses the topological degree of a mapping F: D C R k —► R...
متن کاملA Characterization of Positive Quadrature Formulae
A positive quadrature formula with n nodes which is exact for polynomials of degree In — r — 1, 0 < r < « , is based on the zeros of certain quasi-orthogonal polynomials of degree n . We show that the quasi-orthogonal polynomials that lead to the positive quadrature formulae can all be expressed as characteristic polynomials of a symmetric tridiagonal matrix with positive subdiagonal entries. A...
متن کاملNonstandard Gaussian quadrature formulae based on operator values
In this paper, we develop the theory of so-called nonstandard Gaussian quadrature formulae based on operator values for a general family of linear operators, acting of the space of algebraic polynomials, such that the degrees of polynomials are preserved. Also, we propose a stable numerical algorithm for constructing such quadrature formulae. In particular, for some special classes of linear op...
متن کاملQuadrature formulae for Fourier coefficients
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Michhelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a func...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Evolutionary Bioinformatics
سال: 2006
ISSN: 1176-9343,1176-9343
DOI: 10.1177/117693430600200010