Polynomial evaluation

Support and approximation properties of Hermite splines

Michaël Unser, Julien René Fageot, Shayan Aziznejad, Virginie Sophie Uhlmann

In this paper, we formally investigate two mathematical aspects of Hermite splines that are relevant to practical applications. We first demonstrate that Hermite splines are maximally localized, in the sense that the size of their support is minimal among ...

2020

An Improved Analysis of Local Search for Max-Sum Diversification

Friedrich Eisenbrand, Alfonso Bolívar Cevallos Manzano

We present new techniques to analyze natural local search algorithms for several variants of the max-sum diversification problem which, in its most basic form, is as follows: given an n-point set X subset of R-d and an integer k, select k points in X so th ...

INFORMS2019

Approximation algorithms for geometric dispersion

Alfonso Bolívar Cevallos Manzano

The most basic form of the max-sum dispersion problem (MSD) is as follows: given n points in R^q and an integer k, select a set of k points such that the sum of the pairwise distances within the set is maximal. This is a prominent diversity problem, with w ...

EPFL2016

On the evaluation of hyper-singular double normal derivative kernels in surface integral equation methods

Juan Ramon Mosig, Athanasios Polymeridis

A stable and efficient numerical scheme for the evaluation of surface integrals with 1/R-3-type singularities is presented. The method is based on the combination of the direct evaluation method and the singularity subtraction technique. The proposed metho ...

Elsevier2013

Fast and accurate computation of hyper-singular integrals in Galerkin surface integral equation formulations via the direct evaluation method

Juan Ramon Mosig, Athanasios Polymeridis

Hypersingular 4-D integrals, arising in the Galerkin discretization of surface integral equation formulations, are computed by means of the direct evaluation method. The proposed scheme extends the basic idea of the singularity cancellation methods, usuall ...

Institute of Electrical and Electronics Engineers2011

Efficient machine precision computation of impedance matrix elements in surface integral equation formulations

Juan Ramon Mosig, Athanasios Polymeridis

The direct evaluation program tailored to the singular integrals arising in the first-kind and second-kind Fredholm surface integral equation formulations is presented. The exponential convergence of the proposed technique can safely guarantee the inherite ...

2011