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This paper studies the numerical approximation of solution of the Dirichlet problem for the fully nonlinear Monge-Ampere equation. In this approach, we take the advantage of reformulation the Monge-Ampere problem as an optimization problem,…

Analysis of PDEs · Mathematics 2017-01-20 Fethi Ben Belgacem

This article is about both approximation theory and the numerical solution of partial differential equations (PDEs). First we introduce the notion of {\em reciprocal-log} or {\em log-lightning approximation} of analytic functions with…

Numerical Analysis · Mathematics 2020-10-06 Yuji Nakatsukasa , Lloyd N. Trefethen

An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…

Numerical Analysis · Mathematics 2014-04-30 Ying Li

The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and we show the order…

Numerical Analysis · Mathematics 2019-02-04 Juan Pablo Borthagaray , Leandro M. Del Pezzo , Sandra Martínez

The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…

Numerical Analysis · Mathematics 2016-12-14 Michael V. Klibanov , Dinh-Liem Nguyen , Loc H. Nguyen , Hui Liu

The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection. The alternating projection algorithm of von…

Optimization and Control · Mathematics 2018-09-24 D. Russell Luke

We propose a monotone, and consistent numerical scheme for the approximation of the Dirichlet problem for the normalized Infinity Laplacian, which could be related to the family of so--called two--scale methods. We show that this method is…

Numerical Analysis · Mathematics 2022-09-14 Wenbo Li , Abner J. Salgado

We give integral formulas to approximate solutions of Dirichlet and Neumann problems for Helmholtz equation at high frequencies. These approximations are valid in the complementary of a union of convex compact obstacles. The first step of…

Analysis of PDEs · Mathematics 2014-02-18 François Cuvelier

In this work, we present two numerical schemes for a free boundary problem called one phase quadrature domain. In the first method by applying the proprieties of given free boundary problem, we derive a method that leads to a fast iterative…

Numerical Analysis · Mathematics 2012-03-06 Mahmoudreza Bazarganzadeh , Farid Bozorgnia

A convergent numerical method for $\alpha$-dissipative solutions of the Hunter-Saxton equation is derived. The method is based on applying a tailor-made projection operator to the initial data, and then solving exactly using the generalized…

Numerical Analysis · Mathematics 2025-05-09 Thomas Christiansen , Katrin Grunert , Anders Nordli , Susanne Solem

This application for learning APPROXIMATION ALGORITHM has been designed in Java which will make user comfortable in learning the very complex subject "NP-Completeness" and the solution to NP-Complete problem using approximation algorithm.

Data Structures and Algorithms · Computer Science 2014-01-13 Chiranjeev Kumar

Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…

Optimization and Control · Mathematics 2019-01-25 Ching-pei Lee , Stephen J. Wright

We propose a spectral collocation method to approximate the exact boundary control of the wave equation in a square domain. The idea is to introduce a suitable approximate control problem that we solve in the finite-dimensional space of…

Numerical Analysis · Mathematics 2023-04-17 Somia Boumimez , Carlos Castro

Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…

Numerical Analysis · Computer Science 2014-12-04 Uri Ascher , Farbod Roosta-Khorasani

For initial value problems associated with operator-valued Riccati differential equations posed in the space of Hilbert--Schmidt operators existence of solutions is studied. An existence result known for algebraic Riccati equations is…

Analysis of PDEs · Mathematics 2018-08-06 Monika Eisenmann , Etienne Emmrich , Volker Mehrmann

In this paper, we propose a finite-volume scheme for aggregation-diffusion equations based on a Scharfetter--Gummel approximation of the quadratic, nonlocal flux term. This scheme is analyzed concerning well-posedness and convergence…

Numerical Analysis · Mathematics 2021-05-12 André Schlichting , Christian Seis

We propose a new numerical scheme for Backward Stochastic Differential Equations based on branching processes. We approximate an arbitrary (Lipschitz) driver by local polynomials and then use a Picard iteration scheme. Each step of the…

Numerical Analysis · Mathematics 2017-07-31 Bruno Bouchard , Xiaolu Tan , Xavier Warin , Yiyi Zou

We review recent results obtained to solve fractional order optimal control problems with free terminal time and a dynamic constraint involving integer and fractional order derivatives. Some particular cases are studied in detail. A…

Optimization and Control · Mathematics 2013-06-04 Shakoor Pooseh , Ricardo Almeida , Delfim F. M. Torres

This paper is concerned with the inverse problem of reconstructing small and local perturbations of a planar surface using the field interaction between a known plasmonic particle and the planar surface. The aim is to perform a…

Analysis of PDEs · Mathematics 2018-11-21 Habib Ammari , Doo Sung Choi , Sanghyeon Yu

This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…

Information Theory · Computer Science 2012-11-15 Emmanuel Candes , Carlos Fernandez-Granda