Related papers: Centering Projection Methods for Wavelet Feasibili…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
A {\em vortex pair} solution of the incompressible $2d$ Euler equation in vorticity form $$ \omega_t + \nabla^\perp \Psi\cdot \nabla \omega = 0 , \quad \Psi = (-\Delta)^{-1} \omega, \quad \hbox{in } \mathbb{R}^2 \times (0,\infty)$$ is a…
Adaptive mesh refinement techniques are nowadays an established and powerful tool for the numerical discretization of PDE's. In recent years, wavelet bases have been proposed as an alternative to these techniques. The main motivation for…
The recently proposed empirical wavelet transform was based on a particular type of filter. In this paper, we aim to propose a general framework for the construction of empirical wavelet systems in the continuous case. We define a…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider orbital motion in transverse plane for a single…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
After surveying some known properties of compact convex sets in the plane, we give a two rigorous proofs of the general feeling that supporting lines can be slide-turned slowly and continuously. Targeting a wide readership, our treatment is…
We proved that for any matrix dilation and for any positive integer $n$, there exists a compactly supported tight wavelet frame with approximation order $n$. Explicit methods for construction of dual and tight wavelet frames with a given…
We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended…
We construct directional wavelet systems that will enable building efficient signal representation schemes with good direction selectivity. In particular, we focus on wavelet bases with dyadic quincunx subsampling. In our previous work, We…
We propose a new family of mapped WENO schemes by using several adaptive control functions and a smoothing approximation of the signum function. The proposed schemes introduce the adaptivity and admit an extensive permitted range of the…
We present the application of the variational-wavelet analysis to the quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive)…
We propose a novel projection method to treat near-incompressibility and volumetric locking in small- and large-deformation elasticity and plasticity within the context of higher order material point methods. The material point method is…
In this paper we present the successive centralization of the circumcenter reflection scheme with several control sequences for solving the convex feasibility problem in Euclidean space. Assuming that a standard error bound holds, we prove…
Using the Daubechies conditions of compact support, orthogonal, and regularity, we were able to derive bivariate scaling functions with which to reproduce linear functions (planes). We describe how to create all possible masks of refinement…
In this paper we formulate a weighted version of minimum problem (1.4) on the sphere and we show that, for $K\le L$, if $\set{\phi_k}^K_{k=1}$ consists of the spherical functions with degree less than $N$ we can localize the points…
We construct a directional spin wavelet framework on the sphere by generalising the scalar scale-discretised wavelet transform to signals of arbitrary spin. The resulting framework is the only wavelet framework defined natively on the…
The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on…