Related papers: Approximation of Partially Smooth Functions
The following result was announced in the earlier version(s) of this paper: On weakly compactly generated Banach spaces which admit a Lipschitz, C^{p} smooth bump function, one can uniformly approximate uniformly continuous, bounded,…
If f is a smooth function on a Hodge manifold, we construct a canonical sequence of real algebraic functions that converge to f in the smooth topology. The definition of of the approximants is inspired by Berezin-Toeplitz quantization. The…
In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in $d$ dimensions, where $d$ can be arbitrary. This method is simple, and relies only…
The sparse polynomial approximation of continuous functions has emerged as a prominent area of interest in function approximation theory in recent years. A key challenge within this domain is the accurate estimation of approximation errors.…
We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose less restrictive assumptions on the composite objective functional considering…
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.
In this paper we investigate a problem of approximation of continuous mappings by smooth mappings with nonnegative Jacobian.
In this short, conceptual paper we observe that essentially the same mathematics applies in three contexts with disparate literatures: (1) sigmoidal and RBF approximation of smooth functions, (2) rational approximation of analytic functions…
A mathematical smooth function means that the function has continuous derivatives to a certain degree C(k). We call it a k-smooth function or a smooth function if k can grow infinitively. Based on quantum physics, there is no such smooth…
We describe, in the general setting of closed cone fields, the set of causal functions which can be approximated by smooth Lyapunov. We derive several consequences on causality theory. Dans le contexte g\'en\'eral des champs de cones…
This paper is devoted to filtering, smoothing, and prediction of polynomial processes that are partially observed. These problems are known to allow for an explicit solution in the simpler case of linear Gaussian state space models. The key…
A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the…
The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…
Generic approximation of entire functions by their Pad\'{e} approximants has been achieved in the past (\cite{3}). In the present article we obtain generic approximation of holomorphic functions on arbitrary open sets by sequences of their…
Approximations of non-smooth multivariate functions return low-order approximations in the vicinities of the singularities. Most prior works solve this problem for univariate functions. In this work we introduce a method for approximating…
Extending classical results on polytopal approximation of convex bodies, we derive asymptotic formulas for the weighted approximation of smooth convex functions by piecewise affine convex functions as the number of their facets tends to…
A prevalent problem in general state-space models is the approximation of the smoothing distribution of a state, or a sequence of states, conditional on the observations from the past, the present, and the future. The aim of this paper is…
The goal of this note is to show that continuous functions may be approximated using scattered translates of the Poisson kernel.
In this note, we will present global equisingular approximations of quasi-plurisubharmonic functions with stable analytic pluripolar sets on compact complex manifolds.
Given cell-average data values of a piecewise smooth bivariate function $f$ within a domain $\Omega$, we look for a piecewise adaptive approximation to $f$. We are interested in an explicit and global (smooth) approach. Bivariate…