In this paper, the Kadomtsev-Petviashvili equation is solved by using the Adomian’s decomposition method , modified Adomian’s decomposition method , variational iteration method , modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The existence and uniqueness of the solution and convergence of the proposed...

A surface parameterization is a function that maps coordinates in a 2-dimensional parameter space to points on a surface. This thesis investigates two kinds of parameterizations for surfaces that are disc-like in shape. The first is a map from a region of the plane to the surface. The second is a mapping from one surface to another, which defines a correspondence between them. The main challeng...

In this thesis we do image sequence upscaling using variational methods. We have developed, implemented and tested the three main elements of the upscaling part of a video processor using variational methods plus a non-variational preprocessing method detecting the scan format of the input video. The three upscalings needed are deinterlacing (DI), which is creating the never recorded every othe...

This paper gives an introduction to the use of variational methods in Bayesian inference and shows how variational methods can be used to approximate the intractable posterior distributions which arise in this kind of inference. The flexibility of these approximations allows us to include positivity constraints when attempting to infer hidden pixel intensities in images. The approximating poste...

We consider reinforcement learning as solving a Markov decision process with unknown transition distribution. Based on interaction with the environment, an estimate of the transition matrix is obtained from which the optimal decision policy is formed. The classical maximum likelihood point estimate of the transition model does not reflect the uncertainty in the estimate of the transition model ...

In this paper we introduce four multigrid algorithms for the constrained minimization of non-quadratic functionals. The algorithm introduced in [L. Badea, Convergence rate of a Schwarz multilevel method for the constrained minimization of non-quadratic functionals, SIAM J. Numer. Anal., 44, 2, 2006, p. 449-477], has a sub-optimal computing complexity because the convex set, which is defined on ...

We prove that the AdS/CFT calculation of 1-point functions can be drastically simplified by using variational arguments. We give a simple proof, valid for any theory that can be derived from a Lagrangian, that the large radius divergencies in 1-point functions can always be renormalized away (at least in the semiclassical approximation). The renormalized 1-point functions then follow by a simpl...

Bayesian inference has become increasingly important in statistical machine learning. Exact Bayesian calculations are often not feasible in practice, however. A number of approximate Bayesian methods have been proposed to make such calculations practical, among them the variational Bayesian (VB) approach. The VB approach, while useful, can nevertheless suffer from slow convergence to the approx...