In this paper, we consider the problem of the approximation of the integral of a function f over a d-dimensional simplex S of Rd by some quadrature formulas which use only the functional and derivative values of f on the boundary of the simplex S or function data at the vertices of S, at points on its facets and at its center of gravity. The quadrature formulas are computed by integrating over S a polynomial approximant of f which uses functional and derivative values at the vertices of S.

On Some Numerical Integration Formulas on the d-Dimensional Simplex

Di Tommaso, Filomena
;
2020

Abstract

In this paper, we consider the problem of the approximation of the integral of a function f over a d-dimensional simplex S of Rd by some quadrature formulas which use only the functional and derivative values of f on the boundary of the simplex S or function data at the vertices of S, at points on its facets and at its center of gravity. The quadrature formulas are computed by integrating over S a polynomial approximant of f which uses functional and derivative values at the vertices of S.
Numerical integration, Cubature, Simplex
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/306892
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