Minimal cubature rules and polynomial interpolation in two variables

Polynomial interpolation and cubature over polygons

We have implemented a Matlab code to compute Discrete Extremal Sets (of Fekete and Leja type) on convex or concave polygons, together with the corresponding interpolatory cubature formulas. The method works by QR and LU factorizations of rectangular Vandermonde matrices on Weakly Admissible Meshes (WAMs) of polygons, constructed by polygon quadrangulation. 2000 AMS subject classification: 65D05...

Gaussian Cubature and Bivariate Polynomial Interpolation

Gaussian cubature is used to study bivariate polynomial interpolation based on the common zeros of quasi-orthogonal polynomials.

On polynomial interpolation of two variables

Markov cubature rules for polynomial processes

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment-matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to study the existence of such rules using algebraic techniques. These rules aim to improve the tractab...

Minimal cubature rules on an unbounded domain

A family of minimal cubature rules is established on an unbounded domain, which is the first such family known on unbounded domains. The nodes of such cubature rules are common zeros of certain orthogonal polynomials on the unbounded domain, which are also constructed. 2000 AMS subject classification: 41A05, 65D05, 65D32.