相关论文: Nonlinear Accelerator Problems via Wavelets: 5. Ma…

We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to devise an inversion procedure which has the…

In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…

This article reviews recent developments in multiresolution analysis which make it a powerful tool for the systematic treatment of the multiple length-scales inherent in the electronic structure of matter. Although the article focuses on…

Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…

For the obstacle problem with a nonlinear operator, we characterize the space of global solutions with compact contact sets. This is achieved by constructing a bijection onto a class of quadratic polynomials describing the asymptotic…

I discuss approaches to optimally remove noise from images. A generalization of Wiener filtering to Non-Gaussian distributions and wavelets is described, as well as an approach to measure the errors in the reconstructed images. We argue…

As a main research area in applied and computational harmonic analysis, the theory and applications of framelets have been extensively investigated. Most existing literature is devoted to framelet systems that only use one dilation matrix…

We are interested in the numerical solution of nonsymmetric linear systems arising from the discretization of convection-diffusion partial differential equations with separable coefficients and dominant convection. Preconditioners based on…

Discrete wavelets are applied to parametrization of the intra-chain two-point correlation functions of homopolymers in dilute solutions obtained from Monte Carlo simulation. Several orthogonal and biorthogonal basis sets have been…

Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…

The discretization of the density matrix is proposed as a nonlinear positive map for systems with continuous variables. This procedure is used to calculate the entanglement between two modes through different criteria, such as Tsallis…

This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…

Deep learning models extract, before a final classification layer, features or patterns which are key for their unprecedented advantageous performance. However, the process of complex nonlinear feature extraction is not well understood, a…

We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…

We consider an application of variational-wavelet approach to nonlinear collective models of beam/plasma physics: Vlasov/Boltzmann-like reduction from general BBGKY hierachy. We obtain fast convergent multiresolution representations for…

The discretization of optimal transport problems often leads to large linear programs with sparse solutions. We derive error estimates for the approximation of the problem using convex combinations of Dirac measures and devise an active-set…

We present recent finite element numerical results on a model convection-diffusion problem in the singular perturbed case when the convection term dominates the problem. We compare the standard Galerkin discretization using the linear…

We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…

This report summarizes progress made towards a new approach for enlarging the dynamic aperture of particle accelerators. Unlike prior methods which attempted to move the location of select resonances outward in phase space, our approach…

Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…