Related papers: Sharper and Simpler Nonlinear Interpolants for Pro…
In this article we give a straightforward proof of refined inequalities between Lorentz spaces and Besov spaces and we generalize previous results of H. Bahouri and A. Cohen. Our approach is based in the characterization of Lorentz spaces…
Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For…
We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs $P$ and $Q$ and vocabulary $V$ (set of predicates) the existence of a program $R$ in $V$ such that $P \cup R$ and $P \cup…
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…
The interpolation step in the Guruswami-Sudan algorithm is a bivariate interpolation problem with multiplicities commonly solved in the literature using either structured linear algebra or basis reduction of polynomial lattices. This…
The paper deals with two fundamental types of trigonometric polynomials and splines on uniform grids, which allow us to construct interpolation approximations that depend linearly on the values of the interpolated function. Fundamental on…
Interpolation is an essential tool in software verification, where first-order theories are used to constrain datatypes manipulated by programs. In this paper, we introduce the datatype theory of contiguous arrays with maxdiff, where arrays…
Structured kernel interpolation (SKI) accelerates Gaussian process (GP) inference by interpolating the kernel covariance function using a dense grid of inducing points, whose corresponding kernel matrix is highly structured and thus…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
Despite hundreds of papers on preconditioned linear systems of equations, there remains a significant lack of comprehensive performance benchmarks comparing various preconditioners for solving symmetric positive definite (SPD) systems. In…
In the present work, we study how to develop an efficient solver for the fast resolution of large and sparse linear systems that occur while discretizing elliptic partial differential equations using isogeometric analysis. Our new approach…
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
Several problems of trigonometric approximation on a hexagon and a triangle are studied using the discrete Fourier transform and orthogonal polynomials of two variables. A discrete Fourier analysis on the regular hexagon is developed in…
Using a deterministic framework allows us to estimate a function with the purpose of interpolating data in spatial statistics. Radial basis functions are commonly used for scattered data interpolation in a d-dimensional space, however,…
In this paper we consider the approximation of functions by radial basis function interpolants. There is a plethora of results about the asymptotic behaviour of the error between appropriately smooth functions and their interpolants, as the…
We study schemes for interpolating functions that take values in the special orthogonal group $SO(n)$. Our focus is on interpolation schemes obtained by embedding $SO(n)$ in a linear space, interpolating in the linear space, and mapping the…
Block-to-block interface interpolation operators are constructed for several common high-order finite difference discretizations. In contrast to conventional interpolation operators, these new interpolation operators maintain the strict…
We design and analyze new protocols to verify the correctness of various computations on matrices over the ring F[x] of univariate polynomials over a field F. For the sake of efficiency, and because many of the properties we verify are…
We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete…