Computing Tchakaloff-like cubature rules on spline curvilinear polygons

TitleComputing Tchakaloff-like cubature rules on spline curvilinear polygons
Publication TypeJournal Article
Year of Publication2021
AuthorsSommariva, A, Vianello, M
JournalDolomites Research Notes on Approximation
Volume14
Issue1
Pagination1-11
Date Published01/2021
PublisherPadova University Press
Place PublishedPadova, IT
ISSN Number20356803
Abstract

We present an algorithm that computes a PI-type (Positive Interior) algebraic cubature rule of degree n with at most (n+1)(n+2)=2 nodes, over spline curvilinear polygons. The key ingredients are a theorem by Davis on Tchakaloff discretization sets, a specific in-domain algorithm for such spline polygons and the sparse nonnegative solution of underdetermined moment matching systems by the Lawson-Hanson NonNegative Least Squares solver. A numerical code (implemented in Matlab) is also provided, together with several numerical tests.

URLhttps://drna.padovauniversitypress.it/2021/1/1