Computing Tchakaloff-like cubature rules on spline curvilinear polygons
Title | Computing Tchakaloff-like cubature rules on spline curvilinear polygons |
Publication Type | Journal Article |
Year of Publication | 2021 |
Authors | Sommariva, A, Vianello, M |
Journal | Dolomites Research Notes on Approximation |
Volume | 14 |
Issue | 1 |
Pagination | 1-11 |
Date Published | 01/2021 |
Publisher | Padova University Press |
Place Published | Padova, IT |
ISSN Number | 20356803 |
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. |
URL | https://drna.padovauniversitypress.it/2021/1/1 |
DOI | 10.14658/pupj-drna-2021-1-1 |