Related papers: Variational Approach in Wavelet Framework to Polyn…
In this paper, we introduce and study a class of resolvent dynamical systems to investigate some inertial proximal methods for solving mixed variational inequalities. These proposed methods along with their discretizations and derived rates…
Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…
We present a novel approach for nonparametric regression using wavelet basis functions. Our proposal, $\texttt{waveMesh}$, can be applied to non-equispaced data with sample size not necessarily a power of 2. We develop an efficient proximal…
We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order…
A revised version of the quaternion approach for numerical integration of the equations of motion for rigid polyatomic molecules is proposed. The modified approach is based on a formulation of the quaternion dynamics with constraints. This…
Most applications of Bayesian Inference for parameter estimation and model selection in astrophysics involve the use of Monte Carlo techniques such as Markov Chain Monte Carlo (MCMC) and nested sampling. However, these techniques are time…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…
Some higher-order quasilinear parabolic, hyperbolic, and nonlinear dispersion equations are shown to admit various blow-up, extinction, and travelling wave solutions, which reduce to variational problems admitting countable families of…
New algorithms for fast wavelet transforms with biorthogonal spline wavelets on nonuniform grids are presented. In contrary to classical wavelet transforms, the algorithms are not based on filter coefficients, but on algorithms for B-spline…
We present a new method for the approximate solution of the strongly coupled, nonlinear stress-diffusion problem that appears when modeling hydrogen transport in metals. The most salient feature of the proposed approximation is that it is…
The evaluation of loop amplitudes via differential equations and harmonic polylogarithms is discussed at an introductory level. The method is based on evolution equations in the masses or in the external kinematical invariants and on a…
We extend the varying coefficient functional linear model to the nonlinear model and propose a varying coefficient functional additive model. The proposed method can represent the relationship between functional predictors and a scalar…
This work develops problem statements related to encoders and autoencoders with the goal of elucidating variational formulations and establishing clear connections to information-theoretic concepts. Specifically, four problems with varying…
A variational framework, initially developed for high-order mesh optimisation, is being extended for r-adaptation. The method is based on the minimisation of a functional of the mesh deformation. To achieve adaptation, elements of the…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
Nonconvex optimization problems arise in different research fields and arouse lots of attention in signal processing, statistics and machine learning. In this work, we explore the accelerated proximal gradient method and some of its…
Wavelets are a useful basis for constructing solutions of the integral and differential equations of scattering theory. Wavelet bases efficiently represent functions with smooth structures on different scales, and the matrix representation…
We explore the use of bi-orthogonal basis for continuous wavelet transformations, thus relaxing the so-called admissibility condition on the analyzing wavelet. As an application, we determine the eigenvalues and corresponding radial…
We explore the use of bi-orthogonal basis for continuous wavelet transformations, thus relaxing the so-called admissibility condition on the analyzing wavelet. As an application, we determine the eigenvalues and corresponding radial…