Related papers: Polynomial approximation on disjoint segments and …
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given…
A deep approximation is an approximating function defined by composing more than one layer of simple functions. We study deep approximations of functions of one variable using layers consisting of low-degree polynomials or simple conformal…
We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.
This paper describes a novel method to approximate the polynomial coefficients of regression functions, with particular interest on multi-dimensional classification. The derivation is simple, and offers a fast, robust classification…
Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…
When using images to locate objects, there is the problem of correcting for distortion and misalignment in the images. An elegant way of solving this problem is to generate an error correcting function that maps points in an image to their…
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
Highly efficient and even nearly optimal algorithms have been developed for the classical problem of univariate polynomial root-finding (see, e.g., \cite{P95}, \cite{P02}, \cite{MNP13}, and the bibliography therein), but this is still an…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…
Motivated by conforming finite element methods for elliptic problems of second order, we analyze the approximation of the gradient of a target function by continuous piecewise polynomial functions over a simplicial mesh. The main result is…
Polynomial reproduction plays a relevant role in deriving error estimates for various approximation schemes. Local reproduction in a quasi-uniform setting is a significant factor in the estimation of error and the assessment of stability…
In the paper we consider the problem of multivariate function approximation in polynomial basis. In order to solve this problem, we adjust the least squares method (LSM) by adding information about derivatives of the function. This…
In this work, we propose an interesting method that aims to approximate an activation function over some domain by polynomials of the presupposing low degree. The main idea behind this method can be seen as an extension of the ordinary…
Piecewise constant image approximations of sequential number of segments or clusters of disconnected pixels are treated. The method of majorizing of optimal approximation sequence by hierarchical sequence of image approximations is…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…