 A new recursive formula for integration of polynomial over simplexShaoZhong Lin and ZhiQiang Xie Applied Mathematics and Computation, 2020, vol. 376, issue C Abstract: The simplex integration is a convenient method for the integration over complex domains. It automatically represents the ordinary integral over an arbitrary polyhedron as the algebraic sum of integrals over the oriented simplexes. An existing recursive formula for the integration of monomials over simplex, which was deduced based on special operations of matrices and was presented by the first author of this paper, has significant advantages: not only the computation amount is small, but also the integrals of all the lower order monomials are obtained while computing the integral of the highest order monomial. The extension to a polynomial can be obtained by the linearity of integrals. In this paper, the derivation of the existing recursive formula is detailed. A new recursive formula is emphatically proposed to simplify the existing recursive formula and further increase the speed of computation. The code for computer implementation is also presented. Examples show that the accuracy and efficiency of the recursive formula are higher than numerical integration. Keywords: Analytical integration; Simplex integration; Recursive formula; Polynomials; Polyhedrons; Special operations of matrices (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:376:y:2020:i:c:s0096300320301090 DOI: 10.1016/j.amc.2020.125140 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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