Subperiodic trigonometric subsampling: A numerical approach

We show that Gauss-Legendre quadrature applied to trigonometric poly- nomials on subintervals of the period can be competitive with subperiodic trigonometric Gaussian quadrature. For example with intervals correspond- ing to few angular degrees, relevant for regional scale models on the earth surface, we see a subsampling ratio of one order of magnitude already at moderate trigonometric degrees

Numerical hyperinterpolation over nonstandard planar regions

We discuss an algorithm (implemented in Matlab) that computes numerically total-degree bivariate orthogonal polynomials (OPs) given an algebraic cubature formula with positive weights, and constructs the orthogonal projection (hyperinterpolation) of a function sampled at the cubature nodes. The method is applicable to nonstandard regions where OPs are not known analytically, for example convex and concave polygons, or circular sections such as sectors, lenses and lunes

Caratheodory-Tchakaloff Subsampling

We present a brief survey on the compression of discrete measures by Caratheodory-Tchakaloff Subsampling, its implementation by Linear or Quadratic Programming and the application to multivariate polynomial Least Squares. We also give an algorithm that computes the corresponding Caratheodory-Tchakaloff (CATCH) points and weights for polynomial spaces on compact sets and manifolds in 2D and 3D

Optimal polynomial meshes and Caratheodory-Tchakaloff submeshes on the sphere

Using the notion of Dubiner distance, we give an elementary proof of the fact that good covering point configurations on the 2-sphere are optimal polynomial meshes. From these we extract Caratheodory-Tchakaloff (CATCH) submeshes for compressed Least Squares fitting

Discrete norming inequalities on sections of sphere, ball and torus

By discrete trigonometric norming inequalities on subintervals of the period, we construct norming meshes with optimal cardinality growth for algebraic polynomials on sections of sphere, ball and torus

Compression of multivariate discrete measures and applications

We discuss two methods for the compression of multivariate discrete measures, with applications to node reduction in numerical cubature and least-squares approximation. The methods are implemented in the Matlab computing environment, in dimension two

Legal culture and professional cultures in the prison system

The contribution focuses, with reference to Italy, on the interplay between professional cultures in the field of the prison and tries to describe how the normative characteristics, typical of the professional cultures of teachers and health professionals, meet the total institution. The introduction presents the different sources from which the empirical material comes, collected by the authors in the course of different research and monitoring activities, which allowed them to access to the prison field. The second paragraph introduces the reader to the complexity of the Italian prison system, which has undergone a profound differentiation in recent years. The third paragraph analyzes, on the basis of the qualitative data collected, the encounter between the professional cultures of teachers and doctors and the specific prison culture. The conclusion enlightens the irreducible polymorphism that characterizes the institution and unavoidably interferes with a sociologist’s efforts at generalization

Polynomial fitting and interpolation on circular sections

We construct Weakly Admissible polynomial Meshes (WAMs) on circular sections, such as symmetric and asymmetric circular sectors, circular segments, zones, lenses and lunes. The construction resorts to recent results on subperiodic trigonometric interpolation. The paper is accompanied by a software package to perform polynomial fitting and interpolation at discrete extremal sets on such regions

Polynomial-free unisolvence of polyharmonic splines with odd exponent by random sampling

In a recent paper almost sure unisolvence of RBF interpolation at random points with no polynomial addition was proved, for Thin-Plate Splines and Radial Powers with noninteger exponent. The proving technique left unsolved the case of odd exponents. In this short note we prove almost sure polynomial-free unisolvence in such instances, by a deeper analysis of the interpolation matrix determinant and fundamental properties of analytic functions.Comment: Keywords: multivariate interpolation, Radial Basis Functions, polyharmonic splines, odd integer exponent, unisolvence, analytic function