Adaptive finite element methods with convergence rates
Adaptive Finite Element Methods for numerically solving elliptic equations are used often in
practice. Only recently [12],[17] have these methods been shown to converge. However, this …
practice. Only recently [12],[17] have these methods been shown to converge. However, this …
[PDF][PDF] Approximation classes for adaptive methods
Adaptive Finite Element Methods (AFEM) are numerical procedures that approximate the
solution to a partial differential equation (PDE) by piecewise polynomials on adaptively …
solution to a partial differential equation (PDE) by piecewise polynomials on adaptively …
The Bramble--Hilbert lemma for convex domains
S Dekel, D Leviatan - SIAM journal on mathematical analysis, 2004 - SIAM
The Bramble--Hilbert lemma is a fundamental result on multivariate polynomial
approximation. It is frequently applied in the analysis of finite elements methods (FEM) used …
approximation. It is frequently applied in the analysis of finite elements methods (FEM) used …
An improved image compression algorithm using binary space partition scheme and geometric wavelets
G Chopra, AK Pal - IEEE transactions on image processing, 2010 - ieeexplore.ieee.org
Geometric wavelet is a recent development in the field of multivariate nonlinear piecewise
polynomials approximation. The present study improves the geometric wavelet (GW) image …
polynomials approximation. The present study improves the geometric wavelet (GW) image …
Decomposition of weighted Triebel–Lizorkin and Besov spaces on the ball
Abstract Weighted Triebel–Lizorkin and Besov spaces on the unit ball B d in ℝ d with
weights w μ (x)=(1−| x| 2) μ− 1/2, μ≥ 0, are introduced and explored. A decomposition …
weights w μ (x)=(1−| x| 2) μ− 1/2, μ≥ 0, are introduced and explored. A decomposition …
Whitney estimates for convex domains with applications to multivariate piecewise polynomial approximation
S Dekel, D Leviatan - Foundations of Computational Mathematics, 2004 - Springer
We prove the following Whitney estimate. Given 0< p ≤ ∞, r ∈ N, and d ≥ 1, there exists a
constant C (d, r, p), depending only on the three parameters, such that for every bounded …
constant C (d, r, p), depending only on the three parameters, such that for every bounded …
Adaptive multivariate approximation using binary space partitions and geometric wavelets
S Dekel, D Leviatan - SIAM journal on numerical analysis, 2005 - SIAM
The binary space partition (BSP) technique is a simple and efficient method to adaptively
partition an initial given domain to match the geometry of a given input function. As such, the …
partition an initial given domain to match the geometry of a given input function. As such, the …
Image coding with geometric wavelets
D Alani, A Averbuch, S Dekel - IEEE transactions on image …, 2006 - ieeexplore.ieee.org
This paper describes a new and efficient method for low bit-rate image coding which is
based on recent development in the theory of multivariate nonlinear piecewise polynomial …
based on recent development in the theory of multivariate nonlinear piecewise polynomial …
Optimally sparse image representation by the easy path wavelet transform
The Easy Path Wavelet Transform (EPWT), 20 has recently been proposed by one of the
authors as a tool for sparse representations of bivariate functions from discrete data, in …
authors as a tool for sparse representations of bivariate functions from discrete data, in …
Graph wedgelets: Adaptive data compression on graphs based on binary wedge partitioning trees and geometric wavelets
W Erb - IEEE Transactions on Signal and Information …, 2023 - ieeexplore.ieee.org
We introduce graph wedgelets-a tool for data compression on graphs based on the
representation of signals by piecewise constant functions on adaptively generated binary …
representation of signals by piecewise constant functions on adaptively generated binary …