Related papers: General Optimal Polynomial Approximants, Stabiliza…

We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that…

Using partial derivatives $\partial_zf$ and $\partial_{\ol z}f$, we introduce Besov spaces of polyanalytic functions on the unit disk and on the upper half-plane. We then prove that the dilatations of each function in polyanalytic Besov…

We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…

It is a classical result in rational approximation theory that certain non-smooth or singular functions, such as $|x|$ and $x^{1/p}$, can be efficiently approximated using rational functions with root-exponential convergence in terms of…

Given a system of functions f = (f1, . . . , fd) analytic on a neighborhood of some compact subset E of the complex plane, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of…

We obtain the exact-order estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations in metrics of spaces L_s, 1\leq s<\infty, of classes of 2\pi-periodic functions, whose…

We address the problem of constructing approximations based on orthogonal polynomials that preserve an arbitrary set of moments of a given function without loosing the spectral convergence property. To this aim, we compute the constrained…

This paper studies the probabilistic function approximation problem over reproducing kernel Hilbert spaces. We show the existence and uniqueness of the optimizer under mild assumptions. Furthermore, we generalize the celebrated representer…

In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex)…

We introduce and study the approximation properties of $g$-polynomials, defined as linear combinations of iterated Stieltjes integrals of a constant function. Focusing on the case where the derivator $g$ has finitely many discontinuities,…

We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…

We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.

We propose a flexible approach for computing the resolvent of the sum of weakly monotone operators in real Hilbert spaces. This relies on splitting methods where strong convergence is guaranteed. We also prove linear convergence under…

We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function evaluations for a given precision level typically rely on explicitly constructing an…

Parallel and cyclic projection algorithms are proposed for minimizing the sum of a finite family of convex functions over the intersection of a finite family of closed convex subsets of a Hilbert space. These algorithms are of…

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…

This work studies optimal polynomial approximants (OPAs) in the classical Hardy spaces on the unit disk, $H^p$ ($1 < p < \infty$). In particular, we uncover some estimates concerning the OPAs of degree zero and one. It is also shown that if…

The theory of universal Taylor series can be extended to the case of Pad\'e approximants where the universal approximation is not realized by polynomials any more, but by rational functions, namely the Pad\'e approximants of some power…

We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the…

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.