7 papers · 1 filter
On the role of weak Marcinkiewicz-Zygmund constants in polynomial approximation by orthogonal bases
Congpei An, Alvise Sommariva, Marco Vianello
We compute numerically the Marcinkiewicz-Zygmund constants of cubature rules, with a special attention to their role in polynomial approximation by orthogonal bases. We test…
Effective numerical integration on complex shaped elements by discrete signed measures
Laura Rinaldi, Alvise Sommariva, Marco Vianello
We discuss a cheap and stable approach to polynomial moment-based compression of multivariate measures by discrete signed measures. The method is based on the availability of an or…
Unisolvence of randomized MultiQuadric Kansa collocation for convection-diffusion with mixed boundary conditions
Maryam Mohammadi, Alvise Sommariva, Marco Vianello
We make a further step in the open problem of unisolvence for unsymmetric Kansa collocation, proving that the MultiQuadric Kansa method with fixed collocation points and random fic…
Cheap and stable quadrature on polyhedral elements
Alvise Sommariva, Marco Vianello
We discuss a cheap tetrahedra-free approach to the numerical integration of polynomials on polyhedral elements, based on hyperinterpolation in a bounding box and Chebyshev moment c…
Unisolvence of Kansa collocation for elliptic equations by polyharmonic splines with random fictitious centers
Maryam Mohammadi, Alvise Sommariva, Marco Vianello
We make a further step in the unisolvence open problem for unsymmetric Kansa collocation, proving nonsingularity of Kansa matrices with polyharmonic splines and random fictitious c…
Unisolvence of unsymmetric random Kansa collocation by Gaussians and other analytic RBF vanishing at infinity
Alvise Sommariva, Marco Vianello
We give a short proof of almost sure invertibility of unsymmetric random Kansa collocation matrices by a class of analytic RBF vanishing at infinity, for the Poisson equation with…