Related papers: Interpolation synthesis for quadratic polynomial i…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated to this singular cause. In this paper, we begin by…
We present new techniques for reducing a multivariate sparse polynomial to a univariate polynomial. The reduction works similarly to the classical and widely-used Kronecker substitution, except that we choose the degrees randomly based on…
We introduce a subexponential algorithm for geometric solving of multivariate polynomial equation systems whose bit complexity depends mainly on intrinsic geometric invariants of the solution set. From this algorithm, we derive a new…
We introduce the notion of quadratic hull of a linear code, and give some of its properties. We then show that any symmetric bilinear multiplication algorithm for a finite-dimensional algebra over a field can be obtained by…
An interpolation-based decoding scheme for interleaved subspace codes is presented. The scheme can be used as a (not necessarily polynomial-time) list decoder as well as a probabilistic unique decoder. Both interpretations allow to decode…
A perfect matching in an undirected graph $G=(V,E)$ is a set of vertex disjoint edges from $E$ that include all vertices in $V$. The perfect matching problem is to decide if $G$ has such a matching. Recently Rothvo{\ss} proved the striking…
A function $f\colon\mathbb R\to\mathbb R$ is called \emph{$k$-monotone} if it is $(k-2)$-times differentiable and its $(k-2)$nd derivative is convex. A point set $P\subset\mathbb R^2$ is \emph{$k$-monotone interpolable} if it lies on a…
In this paper, we propose a framework based on sum-of-squares programming to design iterative first-order optimization algorithms for smooth and strongly convex problems. Our starting point is to develop a polynomial matrix inequality as a…
The Euclidean Algorithm is the often forgotten key to rational approximation techniques, including Taylor, Lagrange, Hermite, osculating, cubic spline, Chebyshev, Pade and other interpolation schemes. A unified view of these various…
Tensor interpolation is an essential step for tensor data analysis in various fields of application and scientific disciplines. In the present work, novel interpolation schemes for general, i.e., symmetric or non-symmetric, invertible…
In this paper, we investigate the approximation properties of two types of multiscale finite element methods with oversampling as proposed in [Hou \& Wu, {\textit{J. Comput. Phys.}}, 1997] and [Efendiev, Hou \& Wu, \textit{SIAM J. Numer.…
Vector extrapolation methods are widely used in large-scale simulation studies, and numerous extrapolation-based acceleration techniques have been developed to enhance the convergence of linear and nonlinear fixed-point iterative methods.…
The recently introduced polynomial time integration framework proposes a novel way to construct time integrators for solving systems of first-order ordinary differential equation by using interpolating polynomials in the complex time plane.…
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…
We present a new Monte Carlo algorithm for the interpolation of a straight-line program as a sparse polynomial $f$ over an arbitrary finite field of size $q$. We assume a priori bounds $D$ and $T$ are given on the degree and number of terms…
In this paper we present an efficient algorithm for bivariate interpolation, which is based on the use of the partition of unity method for constructing a global interpolant. It is obtained by combining local radial basis function…
For a function that is analytic on and around an interval, Chebyshev polynomial interpolation provides spectral convergence. However, if the function has a singularity close to the interval, the rate of convergence is near one. In these…
We consider Fokker-Planck equations that interpolate a pair of supersymmetrically related Fokker-Planck equations with constant coefficients. Based on the interesting property of shape-invariance, various one-parameter interpolations of the…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…