Related papers: Algorithms for Nonnegative $C^2(\mathbb{R}^2)$ Int…

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…

We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…

Completely positive factorization (CPF) is a critical task with applications in many fields. This paper proposes a novel method for the CPF. Based on the idea of exterior point iteration, an optimization model is given, which aims to…

Given a nondecreasing function $f$ on $[-1,1]$, we investigate how well it can be approximated by nondecreasing algebraic polynomials that interpolate it at $\pm 1$. We establish pointwise estimates of the approximation error by such…

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…

Adaptive rational interpolation has been designed in the context of image processing as a new nonlinear technique that avoids the Gibbs phenomenon when we approximate a discontinuous function. In this work, we present a generalization to…

We consider the problem of finding the best nonnegative rank-2 approximation of an arbitrary nonnegative matrix. We first revisit the theory, including an explicit parametrization of all possible nonnegative factorizations of a nonnegative…

This is a survey of some results on the structure and classification of normal analytic compactifications of C^2. Mirroring the existing literature, we especially emphasize the compactifications for which the curve at infinity is…

For the nonparametric regression models with covariates contaminated with normal measurement errors, this paper proposes an extrapolation algorithm to estimate the nonparametric regression functions. By applying the conditional expectation…

In this paper, we give new sparse interpolation algorithms for black box univariate and multivariate rational functions h=f/g whose coefficients are integers with an upper bound. The main idea is as follows: choose a proper integer beta and…

For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…

Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…

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…

We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…

The purpose of this paper is to introduce a very efficient algorithm for signal extrapolation. It can widely be used in many applications in image and video communication, e. g. for concealment of block errors caused by transmission errors…

Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.

The nonnegative integer rank of a matrix is a variant of the classical nonnegative rank, introduced in the 1980s, where factorizations are required to have integer entries. While computing nonnegative integer rank is generally very hard, we…

Nonnegative matrix factorization can be used to automatically detect topics within a corpus in an unsupervised fashion. The technique amounts to an approximation of a nonnegative matrix as the product of two nonnegative matrices of lower…

We describe the topology of a general polynomial mapping $f:\Bbb C^2\to\Bbb C^2.$

Nonconvex optimization problems are widespread in modern machine learning and data science. We introduce an extrapolation strategy into a class of preconditioned second-order convex splitting algorithms for nonconvex optimization problems.…