Minimal cubature formulae of trigonometric degree
نویسندگان
چکیده
In this paper we construct minimal cubature formulae of trigonometric degree: we obtain explicit formulae for low dimensions of arbitrary degree and for low degrees in all dimensions. A useful tool is a closed form expression for the reproducing kernels in two dimensions.
منابع مشابه
Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree
We study cubature formulas for d-dimensional integrals with a high trigonometric degree. To obtain a trigonometric degreè in dimension d, we need about d ` =`! function values if d is large. Only a small number of arithmetical operations is needed to construct the cubature formulas using Smolyak's technique. We also compare diierent methods to obtain formulas with high trigonometric degree. Abs...
متن کاملOn minimal cubature formulae for product weight functions 1
We derive in a simple way certain minimal cubature formulae, obtained by Morrow and Patterson [2], and Xu [4], using a different technique. We also obtain in explicit form new near minimal cubature formulae. Then, as a corollary, we get a compact expression for the bivariate Lagrange interpolation polynomials, based on the nodes of the cubature.
متن کاملNear-minimal cubature formulae on the disk
The construction of (near-)minimal cubature formulae on the disk is still a complicated subject on which many results have been published.We restrict ourselves to the case of radial weight functions and make use of a recent connection between cubature and the concept of multivariate spherical orthogonal polynomials to derive a new system of equations defining the nodes and weights of (near-)min...
متن کاملCubature Rules for Harmonic Functions Based on Radon Projections
We construct a class of cubature formulae for harmonic functions on the unit disk based on line integrals over 2n + 1 distinct chords. These chords are assumed to have constant distance t to the center of the disk, and their angles to be equispaced over the interval [0, 2π]. If t is chosen properly, these formulae integrate exactly all harmonic polynomials of degree up to 4n + 1, which is the h...
متن کاملOn the construction of general cubature formula by flat extensions.
We describe a new method to compute general cubature formulae. The problem is initially transformed into the computation of truncated Hankel operators with flat extensions. We then analyze the algebraic properties associated to flat extensions and show how to recover the cubature points and weights from the truncated Hankel operator. We next present an algorithm to test the flat extension prope...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Comput.
دوره 65 شماره
صفحات -
تاریخ انتشار 1996