9 papers
Comparing algebraic cubature rules on spline curved elements
A. Sommariva, M. Vianello
We compare four methods for the construction of algebraic cubature rules on planar elements, whose boundary is tracked by splines. The methods, that we have developed over the last…
On modified anti-Gaussian rules for Jacobi weight functions
Eleonora Denich, Paolo Novati, Alvise Sommariva
Anti-Gaussian formulas represent an efficient tool for a dynamical estimation of the error of the underlying Gaussian rule. When applied to the Jacobi weight function it is known t…
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…
ORTHOCUB: integral and differential cubature rules by orthogonal moments
Laura Rinaldi, Alvise Sommariva, Marco Vianello
We discuss a numerical package, named ORTHOCUB, for the computation of linear functionals of both integral and differential type on multivariate polynomial spaces. The weighted sum…
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…