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.
Computing Tchakaloff-like cubature rules on spline curvilinear polygons
Vianello M., Sommariva A. (2021) "Computing Tchakaloff-like cubature rules on spline curvilinear polygons " Dolomites Research Notes on Approximation, 14(1), 1-11. DOI: 10.14658/PUPJ-DRNA-2021-1-1
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Dolomites Research Notes on Approximation
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