Related papers: Interpolation Error Estimates for Harmonic Coordin…
A closed convex polytope in n dimensions defined by m linear inequality constraints is considered. If L is a straight line drawn in any direction from any feasible point P, then in general, it intersects every constraint at one point,…
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…
A discrete Fourier analysis on the dodecahedron is studied, from which results on a tetrahedron is deduced by invariance. The results include Fourier analysis in trigonometric functions, interpolation and cubature formulas on these domains.…
Interpolation methodologies have been widely used within the domain of indoor positioning systems. However, existing indoor positioning interpolation algorithms exhibit several inherent limitations, including reliance on complex…
We present an effective harmonic density interpolation method for the numerical evaluation of singular and nearly singular Laplace boundary integral operators and layer potentials in two and three spatial dimensions. The method relies on…
This article presents novel proof methods for estimating interpolation errors, predicated on the understanding that one has already studied foundational error analysis using the finite element method.
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
We construct a quasi-polynomial time deterministic approximation algorithm for computing the volume of an independent set polytope with restrictions. Randomized polynomial time approximation algorithms for computing the volume of a convex…
In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for…
This is the second lecture note on the error analysis of interpolation on simplicial elements without the shape regularity assumption (the previous one is arXiv:1908.03894). In this manuscript, we explain the error analysis of Lagrange…
The problem of finding a triangulation of a convex three-dimensional polytope with few tetrahedra is proved to be NP-hard. We discuss other related complexity results.
Corrections of gradient errors in the interactions regions (IRs) of high energy colliders have traditionally been made by changing the strengths of quadrupoles that are common to both beams, such as the triplet quadrupoles. This article…
We present structures comprised of identical convex polyhedra which are interlocked geometrically. These sets cannot be disassembled by removing individual polyhedra by translations and/or rotations. The shapes that permit interlocking…
In this paper we present a new algorithm for multivariate interpolation of scattered data sets lying in convex domains $\Omega \subseteq \RR^N$, for any $N \geq 2$. To organize the points in a multidimensional space, we build a $kd$-tree…
Explicit pointwise error bounds for the interpolation of a smooth function by piecewise exponential splines of order four are given. Estimates known for cubic splines are extended to a natural class of piecewise exponential splines which…
The triangulations of a regular convex polygon are enumerated according to the number of diagonals parallel to a fixed edge. The enumeration uses the Shapiro convolution identity, as well as an interpretation of this identity in terms of…
In this paper, we determine the topology of the spaces of convex polyhedra inscribed in the unit $2$-sphere and the spaces of strictly Delaunay geodesic triangulations of the unit $2$-sphere. These spaces can be regarded as discretized…
This article gives a ``fundamental solution'' based energy-norm harmonic interpolation approach for two half-space settings of interest: the upper-half $\mathbb{R}^n$ plane, where fundamental solutions satisfy Laplace's equation, and the…
Strata of translation surfaces are covered by the closures of finitely many iso-Delaunay regions: open subspaces parametrizing surfaces whose Delaunay triangulations are combinatorially equivalent. We prove that the iso-Delaunay regions for…
In CAGD the design of a surface that interpolates an arbitrary quadrilateral mesh is definitely a challenging task. The basic requirement is to satisfy both criteria concerning the regularity of the surface and aesthetic concepts. With…