Related papers: Superoscillations with arbitrary polynomial shape
We present a new simple method for rounding a semidefinite programming relaxation of a constraint satisfaction problem. We apply it to the problem of approximate angular synchronization. Specifically, we are given directed distances on a…
We present explicit constructions of orthogonal polynomials inside quadratic bodies of revolution, including cones, hyperboloids, and paraboloids. We also construct orthogonal polynomials on the surface of quadratic surfaces of revolution,…
Based on the Fourier extension, we propose an oversampling collocation method for solving the elliptic partial differential equations with variable coefficients over arbitrary irregular domains. This method only uses the function values on…
The density of polynomials in a weighted space of infinitely differentiable functions in a multidimensional real space is proved under minimal conditions on weight functions and on differences between weight functions. We apply this result…
This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…
This paper presents a novel method for generating a single polynomial approximation that produces correctly rounded results for all inputs of an elementary function for multiple representations. The generated polynomial approximation has…
Instead of sampling a function at a single point, average sampling takes the weighted sum of function values around the point. Such a sampling strategy is more practical and more stable. In this note, we present an explicit method with an…
The possibilities for limit functions on a Fatou component for the iteration of a single polynomial or rational function are well understood and quite restricted. In non-autonomous iteration, where one considers compositions of arbitrary…
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…
Consider the representations of an algebraic group G. In general, polynomial invariant functions may fail to separate orbits. The invariant subring may not be finitely generated, or the number and complexity of the generators may grow…
We propose a general framework for geometric approximation of circular arcs by parametric polynomial curves. The approach is based on constrained uniform approximation of an error function by scalar polynomials. The system of nonlinear…
The vector space of all polynomial functions of degree $k$ on a box of dimension $n$ is of dimension ${n \choose k}$. A consequence of this fact is that a function can be approximated on vertices of the box using other vertices to higher…
We consider polynomials of a few linear forms and show how exploit this type of sparsity for optimization on some particular domains like the Euclidean sphere or a polytope. Moreover, a simple procedure allows to detect this form of…
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…
We introduce two explicit examples of polynomials orthogonal on the unit circle. Moments and the reflection coefficients are expressed in terms of Jacobi elliptic functions. We find explicit expression for these polynomials in terms of a…
We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with $\alpha$-H\"older derivatives (for some $0<\alpha\leq 1$). The smooth approximation is given by means of an…
The polynomial algebra is a deformed SU(2) algebra. Here, we use polynomial algebra as a method to solve a series of deformed oscillators. Meanwhile, we find a series of physics systems corresponding with polynomial algebra with different…
We investigate a way to approximate the maximum of a polynomial over a polytopal region by using Handelman's polynomial decomposition and continuous multivariate generating functions. The maximization problem is NP-hard, but our…
Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…
We study approximation of functions by algebraic polynomials in the H\"older spaces corresponding to the generalized Jacobi translation and the Ditzian-Totik moduli of smoothness. By using modifications of the classical moduli of…