A class of weight functions that admit Tchebycheff quadrature.
نویسندگان
چکیده
منابع مشابه
On weight functions which admit explicit Gauss-Turán quadrature formulas
The main purpose of this paper is the construction of explicit Gauss-Turán quadrature formulas: they are relative to some classes of weight functions, which have the peculiarity that the corresponding s-orthogonal polynomials, of the same degree, are independent of s. These weights too are introduced and discussed here. Moreover, highest-precision quadratures for evaluating Fourier-Chebyshev co...
متن کاملOn a class of weak Tchebycheff systems
In this paper we study the approximation power, the existence of a normalized B-basis and the structure of a degree-raising process for spaces of the form span < 1, x, . . . , x, u(x), v(x) >, requiring suitable assumptions on the functions u and v. The results about degree raising are detailed for special spaces of this form which have been recently introduced in the area of CAGD.
متن کاملStieltjes polynomials and related quadrature formulae for a class of weight functions
Consider a (nonnegative) measure dσ with support in the interval [a, b] such that the respective orthogonal polynomials, above a specific index `, satisfy a three-term recurrence relation with constant coefficients. We show that the corresponding Stieltjes polynomials, above the index 2` − 1, have a very simple and useful representation in terms of the orthogonal polynomials. As a result of thi...
متن کاملSzegö quadrature formulas for certain Jacobi-type weight functions
In this paper we are concerned with the estimation of integrals on the unit circle of the form ∫ 2π 0 f(eiθ)ω(θ)dθ by means of the so-called Szegö quadrature formulas, i.e., formulas of the type ∑n j=1 λjf(xj) with distinct nodes on the unit circle, exactly integrating Laurent polynomials in subspaces of dimension as high as possible. When considering certain weight functions ω(θ) related to th...
متن کاملEfficient quadrature rules for a class of cordial Volterra integral equations: A comparative study
A natural algorithm with an optimal order of convergence is proposed for numerical solution of a class of cordial weakly singular Volterra integral equations. The equations of this class appear in heat conduction problems with mixed boundary conditions. The algorithm is based on a representation of the solution and compound Gaussian quadrature rules with graded meshes. A comparative stud...
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: Michigan Mathematical Journal
سال: 1966
ISSN: 0026-2285
DOI: 10.1307/mmj/1028999599