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 |
