Related papers: Numerical cubature and hyperinterpolation over Sph…
Given a polynomial system f associated with a simple multiple zero x of multiplicity {\mu}, we give a computable lower bound on the minimal distance between the simple multiple zero x and other zeros of f. If x is only given with limited…
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of…
A challenge - and opportunity - is offered to the Hubbard Model community of solutions extant for the strong coupling region. A rigorous and quantitatively demanding test - a Computer Lab - is presented based on certain exact results for…
Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc. R. Soc. Lond. A 8 January 2004 vol. 460 no. 2041 169-198] provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More…
Quadratic permutation polynomial interleavers over integer rings have recently received attention in practical turbo coding systems from deep space applications to mobile communications. In this correspondence, a necessary and sufficient…
We present and analyze an approximation scheme for a class of highly oscillatory kernel functions, taking the 2D and 3D Helmholtz kernels as examples. The scheme is based on polynomial interpolation combined with suitable pre- and…
In this paper, we propose a parallel optimization method for electronic structure calculations based on a single orbital-updating approximation. It is shown by our numerical experiments that the method is efficient and reliable for atomic…
We consider an application involving a financial quadratic portfolio of options, when the joint underlying log-returns changes with multivariate elliptic distribution. This motivates the needs for methods for the approximation of multiple…
This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…
This paper presents some algorithmic techniques to compute explicitly the noetherian operators associated to a class of ideals and modules over a polynomial ring. The procedures we include in this work can be easily encoded in computer…
The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…
A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. A key aspect of this approach is that it…
We develop a collection of numerical algorithms which connect ideas from polyhedral geometry and algebraic geometry. The first algorithm we develop functions as a numerical oracle for the Newton polytope of a hypersurface and is based on…
We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many…
We study multivariate numerical integration of smooth functions in weighted Sobolev spaces with dominating mixed smoothness $\alpha\geq 2$ defined over the $s$-dimensional unit cube. We propose a new quasi-Monte Carlo (QMC)-based quadrature…
Polynomial meshes (called sometimes "norming sets") allow us to estimate the supremum norm of polynomials on a fixed compact set by the norm on its discrete subset. We give a general construction of polynomial weakly admissible meshes on…
The goal of the paper is to establish cubature formulas on combinatorial graphs. Two types of cubature formulas are developed. Cubature formulas of the first type are exact on spaces of variational splines on graphs. Since badlimited…
In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…