Stable integration rules with scattered integration points
نویسنده
چکیده
A general method for near-best approximations to functionals on R, using scattered-data information, is applied for producing stable multidimensional integration rules. The rules are constructed to be exact for polynomials of degree 6m and, for a quasi-uniform distribution of the integration points, it is shown that the approximation order is O(h) where h is an average distance between the data points. c © 1999 Elsevier Science B.V. All rights reserved.
منابع مشابه
Creating stable quadrature rules with preassigned points by interpolation
Anew approach for creating stable quadrature rules with preassigned points is proposed. The idea is to approximate a known stable quadrature rule by a local interpolation at the preassigned points. The construction cost of the method does not grow as the number of the preassigned points increases. The accuracy of the rule depends only on the accuracy of the chosen stable rule and that of the in...
متن کاملNumerical integration using spline quasi-interpolants
In this paper, quadratic rules for obtaining approximate solution of definite integrals as well as single and double integrals using spline quasi-interpolants will be illustrated. The method is applied to a few test examples to illustrate the accuracy and the implementation of the method.
متن کاملStable high-order quadrature rules with equidistant points
Newton-Cotes quadrature rules are based on polynomial interpolation in a set of equidistant points. They are very useful in applications where sampled function values are only available on a regular grid. Yet, these rules rapidly become unstable for high orders. In this paper we review two techniques to construct stable high-order quadrature rules using equidistant quadrature points. The stabil...
متن کاملMultidimensional Lobachevsky Spline Integration on Scattered Data
This paper deals with the topic of numerical integration on scattered data in Rd , d ≤ 10, by a class of spline functions, called Lobachevsky splines. Precisely, we propose new integration formulas based on Lobachevsky spline interpolants, which take advantage of being expressible in the multivariate setting as a product of univariate integrals. Theoretically, Lobachevsky spline integration for...
متن کاملApplication of CAS wavelet to construct quadrature rules for numerical integration
In this paper, based on CAS wavelets we present quadrature rules for numerical solution of double and triple integrals with variable limits of integration. To construct new method, first, we approximate the unknown function by CAS wavelets. Then by using suitable collocation points, we obtain the CAS wavelet coefficients that these coefficients are applied in approximating the unk...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998