Polynomial integration on regions defined by a triangle and a conic

2010/05/06 by David Sevilla, Sevilla, David, Daniel Wachsmuth +1
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #G.1.8 #I.1.2 #Optimization and Control (math.OC) #Symbolic Computation (cs.SC) #cs.SC #math.OC

paper · pdf · doi:10.48550/arxiv.1005.0990

8 pages, accepted by ISSAC 2010

arxiv created 2010/05/06 · arxiv updated 2010/05/07

Abstract

We present an efficient solution to the following problem, of relevance in a numerical optimization scheme: calculation of integrals of the type \iint_T ∩ \f≥0\ ϕ₁ϕ₂ dx dy for quadratic polynomials f,ϕ₁,ϕ₂ on a plane triangle T. The naive approach would involve consideration of the many possible shapes of T∩\f≥0\ (possibly after a convenient transformation) and parameterizing its border, in order to integrate the variables separately. Our solution involves partitioning the triangle into smaller triangles on which integration is much simpler.

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