Related papers: Stable extrapolation of analytic functions
The problem of optimal estimation of functionals $A\xi =\sum\nolimits_{k=0}^{\infty }{}a(k)\xi (k)$ and ${{A}_{N}}\xi =\sum\nolimits_{k=0}^{N}{}a(k)\xi (k)$ which depend on the unknown values of stochastic sequence $\xi (k)$ with stationary…
Tempering is a popular tool in Bayesian computation, being used to transform a posterior distribution $p_1$ into a reference distribution $p_0$ that is more easily approximated. Several algorithms exist that start by approximating $p_0$ and…
We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a…
For a truncated stochastically perturbed equation $x_{n+1}=\max\{ f(x_n)+l\chi_{n+1}, 0 \}$ with $f(x)<x$ on $(0,m)$, which corresponds to the Allee effect, we observe that for very small perturbation amplitude $l$, the eventual behavior is…
Fractional relaxation equations, as well as relaxation functions time-changed by independent stochastic processes have been widely studied (see, for example, \cite{MAI}, \cite{STAW} and \cite{GAR}). We start here by proving that the…
By applying new functional analysis tools in the framework of Fourier interpolation formulas, such as sc-Fredholm operators and Schauder frames, we are able to improve and refine several properties of these aforementioned formulas on the…
In this paper the interpolating rational functions introduced by Floater and Hormann are generalized leading to a whole new family of rational functions depending on $\gamma$, an additional positive integer parameter. For $\gamma = 1$, the…
In this paper, we study the problem of interpolating a continuous function at $(n+1)$ equally-spaced points in the interval $[0,1]$, using shifts of a kernel on the $(1/n)$-spaced infinite grid. The archetypal example here is approximation…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
In this paper, we explore a specific optimization problem that involves the combination of a differentiable nonconvex function and a nondifferentiable function. The differentiable component lacks a global Lipschitz continuous gradient,…
This paper proposes a novel variant of hyperinterpolation, called hard thresholding hyperinterpolation. This approximation scheme of degree $n$ leverages a hard thresholding operator to filter all hyperinterpolation coefficients, which…
A classical result states that every lower bounded superharmonic function on $\Bbb R^2$ is constant. In this paper the following (stronger) one-circle version is proven. If $f\colon \Bbb R^2\to (-\infty,\infty]$ is lower semicontinuous,…
Let $f\in \ell^2(\mathbb Z)$. Define the average of $ f$ over the square integers by $ A_N f(x):=\frac{1}{N}\sum_{k=1}^N f(x+k^2) $. We show that $ A_N$ satisfies a local scale-free $ \ell ^{p}$-improving estimate, for $ 3/2 < p \leq 2$:…
We characterise interpolating and sampling sequences for the spaces of entire functions f such that f e^{-phi} belongs to L^p(C), p>=1 (and some related weighted classes), where phi is a subharmonic weight whose Laplacian is a doubling…
Let T be the unit circle, f be an \alpha-Holder continuous function on T, \alpha>1/2, and A be the algebra of continuous function in the closed unit disk \bar D that are holomorphic in D. Then f extends to a meromorphic function in D with…
We present an $\ell^2_2+\ell_1$-regularized discrete least squares approximation over general regions under assumptions of hyperinterpolation, named hybrid hyperinterpolation. Hybrid hyperinterpolation, using a soft thresholding operator…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
We obtain a result concerning the stability under the interpolation with functional parameter method for the approximation spaces of Lorentz-Marcinkiewicz type and also for the approximation spaces generated by symmetric norming functions…
In this document I develop a weight function theory of positive order basis function interpolants and smoothers. **In Chapter 1 the basis functions and data spaces are defined directly using weight functions. The data spaces are used to…
In this paper we consider the approximation of functions by radial basis function interpolants. There is a plethora of results about the asymptotic behaviour of the error between appropriately smooth functions and their interpolants, as the…