Error Bound of Certain Gaussian Quadrature Rules for Trigonometric Polynomials

نویسندگان

  • MARIJA P. STANIĆ
  • ALEKSANDAR S. CVETKOVIĆ
  • TATJANA V. TOMOVIĆ
چکیده

In this paper we give error bound for quadrature rules of Gaussian type for trigonometric polynomials with respect to the weight function w(x) = 1+cosx, x ∈ (−π, π), for 2π-periodic integrand, analytic in a circular domain. Obtained theoretical bound is checked and illustrated on some numerical examples.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Intractability Results for Positive Quadrature Formulas and Extremal Problems for Trigonometric Polynomials

Lower bounds for the error of quadrature formulas with positive weights are proved. We get intractability results for quasi-Monte Carlo methods and, more generally, for positive formulas. We consider general classes of functions but concentrate on lower bounds for relatively small classes of trigonometric polynomials. We also conjecture that similar lower bounds hold for arbitrary quadrature fo...

متن کامل

Trigonometric Gaussian quadrature on subintervals of the period

We construct a quadrature formula with n+ 1 angles and positive weights, exact in the (2n+1)-dimensional space of trigonometric polynomials of degree ≤ n on intervals with length smaller than 2π. We apply the formula to the construction of product Gaussian quadrature rules on circular sectors, zones, segments and lenses. 2000 AMS subject classification: 65D32.

متن کامل

Trigonometric Multiple Orthogonal Polynomials of Semi-integer Degree and the Corresponding Quadrature Formulas

Abstract. An optimal set of quadrature formulas with an odd number of nodes for trigonometric polynomials in Borges’ sense [Numer. Math. 67 (1994), 271–288], as well as trigonometric multiple orthogonal polynomials of semi-integer degree are defined and studied. The main properties of such a kind of orthogonality are proved. Also, an optimal set of quadrature rules is characterized by trigonome...

متن کامل

Some Remarks on the Construction of Extended Gaussian Quadrature Rules

We recall some results from a paper by Szego on a class of polynomials which are related to extended Gaussian quadrature rules. We show that a very efficient algorithm, for the computation of the abscissas of the rules in question, was already described in that paper. We also point out that this method extends to rules for integrals with an ultraspherical-type weight function. A bound for the e...

متن کامل

Trigonometric Orthogonal Systems and Quadrature Formulae with Maximal Trigonometric Degree of Exactness

Turetzkii [Uchenye Zapiski, Vypusk 1 (149) (1959), 31–55, (English translation in East J. Approx. 11 (2005) 337–359)] considered quadrature rules of interpolatory type with simple nodes, with maximal trigonometric degree of exactness. For that purpose Turetzkii made use of orthogonal trigonometric polynomials of semi–integer degree. Ghizzeti and Ossicini [Quadrature Formulae, Academie-Verlag, B...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012