منابع مشابه
Trigonometric and Gaussian Quadrature
Some relationships are established between trigonometric quadrature and various classical quadrature formulas. In particular Gauss-Legendre quadrature is shown to be a limiting case of trigonometric quadrature. In an earlier paper [1] it was noted that there exist trigonometric and exponential analogs of Gaussian quadrature formulas. We now extend those results to show several interesting featu...
متن کاملTrigonometric 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 کاملError Bound of Certain Gaussian Quadrature Rules for Trigonometric Polynomials
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.
متن کاملSubperiodic trigonometric interpolation and quadrature
We study theoretically and numerically trigonometric interpolation on symmetric subintervals of [−π, π], based on a family of Chebyshevlike angular nodes (subperiodic interpolation). Their Lebesgue constant increases logarithmically in the degree, and the associated Fejérlike trigonometric quadrature formula has positive weights. Applications are given to the computation of the equilibrium meas...
متن کاملPositive trigonometric quadrature formulas and quadrature on the unit circle
We give several descriptions of positive quadrature formulas which are exact for trigonometric-, respectively, Laurent polynomials of degree less or equal to n − 1 − m, 0 ≤ m ≤ n − 1. A complete and simple description is obtained with the help of orthogonal polynomials on the unit circle. In particular it is shown that the nodes polynomial can be generated by a simple recurrence relation. As a ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1970
ISSN: 0025-5718
DOI: 10.2307/2004833