Related papers: Analytical approximation schemes for solving exact…
We consider adaptive approximations of the parameter-to-solution map for elliptic operator equations depending on a large or infinite number of parameters, comparing approximation strategies of different degrees of nonlinearity: sparse…
Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally…
In this paper we study an unconventional inexact Augmented Lagrangian Method (ALM) for convex optimization problems, as first proposed by Bertsekas, wherein the penalty term is a potentially non-Euclidean norm raised to a power between one…
In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More…
Complex polynomial optimization has recently gained more and more attention in both theory and practice. In this paper, we study the optimization of a real-valued general conjugate complex form over various popular constraint sets including…
An approximation method, namely, the Extended Wronskian Determinant Approach, is suggested to study the one-dimensional Dirac equation. An integral equation which can be solved by iterative procedure to find the wave functions is…
A new weak Galerkin (WG) finite element method for solving the biharmonic equation in two or three dimensional spaces by using polynomials of reduced order is introduced and analyzed. The WG method is on the use of weak functions and their…
A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic…
This paper addresses enforcing non-vanishing constraints for solutions to a second order elliptic partial differential equation by appropriate choices of boundary conditions. We show that, in dimension $d\geq2$, under suitable regularity…
This note provides a new perspective on Polchinski's exact renormalization group, by explaining how it gives rise, via the multiscale Bakry-\'Emery criterion, to Lipschitz transport maps between Gaussian free fields and interacting quantum…
This work considers stochastic Galerkin approximations of linear elliptic partial differential equations (PDEs) with stochastic forcing terms and stochastic diffusion coefficients, that cannot be bounded uniformly away from zero and…
In the article we propose a general scheme for solutions of some approximation problems under a rather general setting. We illustrate the application of the proposed scheme by a series of examples, in particular we show that many results in…
The truncation scheme dependence of the exact renormalization group equations is investigated for scalar field theories in three dimensions. The exponents are numerically estimated to the next-to-leading order of the derivative expansion.…
Within the Local Potential Approximation to Wilson's, or Polchinski's, exact renormalization group, and for general spacetime dimension, we construct a function, c, of the coupling constants; it has the property that (for unitary theories)…
The conforming finite element Galerkin method is applied to discretise in the spatial direction for a class of strongly nonlinear parabolic problems. Using elliptic projection of the associated linearised stationary problem with Gronwall…
We derive a priori error estimates for Nitsche's method applied to elliptic problems on approximate domains. Such approximations arise, for example, in unfitted finite element methods, data-driven simulations, and evolving domain problems,…
We present a new approximation scheme for the centrifugal term to solve the Schrodinger equation with the Hulthen potential for any arbitrary l state by means of a mathematical Nikiforov-Uvarov (NU) method. We obtain the bound state energy…
This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of…
In statistics, experimental designs are methods for making efficient experiments. E-optimal designs are the multisets of experimental conditions which minimize the maximum axis of the confidence ellipsoid of estimators. The aim of this…
We establish convergence rates for a fully discrete, multi-level, linear collocation method solving parametric elliptic PDEs on bounded polygonal domains with log-normal inputs. The method uses a finite set of function evaluations in the…