Related papers: Adaptive Quarklet Tree Approximation
This paper deals with near-best approximation of a given bivariate function using elements of quarkonial tensor frames. For that purpose we apply anisotropic tensor products of the univariate B-spline quarklets introduced around 2017 by…
We survey the main results of approximation theory for adaptive piecewise polynomial functions. In such methods, the partition on which the piecewise polynomial approximation is defined is not fixed in advance, but adapted to the given…
In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution…
In this paper, we study a newly developed shearlet system on bounded domains which yields frames for $H^s(\Omega)$ for some $s\in \mathbb{N}$, $\Omega \subset \mathbb{R}^2$. We will derive approximation rates with respect to $H^s(\Omega)$…
This paper addresses the problem of finding a B-term wavelet representation of a given discrete function $f \in \real^n$ whose distance from f is minimized. The problem is well understood when we seek to minimize the Euclidean distance…
Motivated by conforming finite element methods for elliptic problems of second order, we analyze the approximation of the gradient of a target function by continuous piecewise polynomial functions over a simplicial mesh. The main result is…
Using function approximation to represent a value function is necessary for continuous and high-dimensional state spaces. Linear function approximation has desirable theoretical guarantees and often requires less compute and samples than…
We devise a generalization of tree approximation that generates conforming meshes, i.e., meshes with a particular structure like edge-to-edge triangulations. A key feature of this generalization is that the choices of the cells to be…
We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and…
In this paper, we analyze the error estimate of a wavelet frame based image restoration method from degraded and incomplete measurements. We present the error between the underlying original discrete image and the approximate solution which…
In the paper we design a Parseval wavelet frame with a compact support. The corresponding refinement mask uniformly approximates an arbitrary continuous periodic function $f$, $f(0)=1$, $|f(x)|^2+|f(x+\pi)|^2\le 1$. The refinable function…
In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…
This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analyzes its convergence properties. It is established that…
In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…
In this article we prove that it is possible to construct, using newest-vertex bisection, meshes that equidistribute the error in $H^1$-norm, whenever the function to approximate can be decomposed as a sum of a regular part plus a singular…
Let $\{(X_i,Y_i)\}_{i\in \{1,..., n\}}$ be an i.i.d. sample from the random design regression model $Y=f(X)+\epsilon$ with $(X,Y)\in [0,1]\times [-M,M]$. In dealing with such a model, adaptation is naturally to be intended in terms of…
This work is concerned with the study of asymptotic properties of nonparametric density estimates in the framework of circular data. The estimation procedure here applied is based on wavelet thresholding methods: the wavelets used are the…
We propose a dynamic programming algorithm for projection onto wavelet tree structures. In contrast to other recently proposed algorithms which only give approximate tree projections for a given sparsity, our algorithm is guaranteed to…
In \cite{liu2022practical}, a general algorithm is developed to efficiently obtain the best accuracy using the regular refinement. The adaptive refinement allows for obtaining an accuracy with a smaller number of DoFs compared with the…
Within the area of applied harmonic analysis, various multiscale systems such as wavelets, ridgelets, curvelets, and shearlets have been introduced and successfully applied. The key property of each of those systems are their (optimal)…