Related papers: Polynomial approximation of piecewise analytic fun…

We obtain closed expressions for weighted orthogonal polynomials and optimal approximants associated with the function $f(z)=1-\frac{1}{\sqrt{2}}(z_1+z_2)$ and a scale of Hilbert function spaces in the unit $2$-ball having reproducing…

This paper analyzes the approximation properties of spaces of piece-wise tensor product polynomials over box meshes with a focus on application to IsoGeometric Analysis (IGA). The errors are measured in Lebesgue norms. Estimates of…

In this paper, in a multivariate setting we derive near optimal rates of convergence in the minimax sense for estimating partial derivatives of the mean function for functional data observed under a fixed synchronous design over H\"older…

The quasi--equilibrium approximation is employed as a systematic tool for solving the problem of deriving constitutive equations from kinetic models of liquid--crystalline polymers. It is demonstrated how kinetic models of…

We prove a.s. (almost sure) unisolvency of interpolation by continuous random sampling with respect to any given density, in spaces of multivariate a.e. (almost everywhere) analytic functions. Examples are given concerning polynomial and…

We introduce polystar bodies: compact starshaped sets whose gauge or radial functions are expressible by polynomials, enabling tractable computations, such as that of intersection bodies. We prove that polystar bodies are uniformly dense in…

In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange…

Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…

In this paper, we construct an algorithm for minimising piecewise smooth functions for which derivative information is not available. The algorithm constructs a pair of quadratic functions, one on each side of the point with smallest known…

We give polynomial-time approximation schemes for monotone maximization problems expressible in terms of distances (up to a fixed upper bound) and efficiently solvable in graphs of bounded treewidth. These schemes apply in all fractionally…

The paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction…

We discuss technical results on learning function approximations using piecewise-linear basis functions, and analyze their stability and convergence using nonlinear contraction theory.

We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…

Non-smoothness at optimal points is a common phenomenon in many eigenvalue optimization problems. We consider two recent algorithms to minimize the largest eigenvalue of a Hermitian matrix dependent on one parameter, both proven to be…

We consider the class of polynomial optimization problems $\inf \{f(x):x\in K\}$ for which the quadratic module generated by the polynomials that define $K$ and the polynomial $c-f$ (for some scalar $c$) is Archimedean. For such problems,…

In this paper we show that the non-analyticity locus of an arc-analytic function is arc-symmetric. Recall that a function is called arc-analytic if it is real analytic on each real analytic arc. By a result of Bierstone and Milman a big…

Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA and greedy Thiele algorithms have sparked renewed interest…

We focus on the presence of almost automorphy in strongly monotone skew-product semiflows on Banach spaces. Under the $C^1$-smoothness assumption, it is shown that any linearly stable minimal set must be almost automorphic. This extends the…

If a function $f$, acting on a Euclidean space $\mathbb{R}^n$, is "almost" orthogonally additive in the sense that $f(x+y)=f(x)+f(y)$ for all $(x,y)\in\bot\setminus Z$, where $Z$ is a "negligible" subset of the $(2n-1)$-dimensional manifold…

This paper concerns the notion of a symmetric algebra and its generalization to a quasi-symmetric algebra. We study the structure of these algebras in respect to their hull-kernel regularity and existence of some ideals, especially the…