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Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…

Optimization and Control · Mathematics 2025-02-12 Erik Troedsson , Marcus Carlsson , Herwig Wendt

In this paper we analyze a nonconforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. The spaces under consideration lead to a divergence-free method which is…

Numerical Analysis · Mathematics 2024-12-24 Dibyendu Adak , Felipe Lepe , Gonzalo Rivera

In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…

Numerical Analysis · Mathematics 2012-11-16 Jun Fang , Xingyu Gao , Aihui Zhou

We present a novel, global algorithm for solving polynomial multiparameter eigenvalue problems (PMEPs) by leveraging a hidden variable tensor Dixon resultant framework. Our method transforms a PMEP into one or more univariate polynomial…

Numerical Analysis · Mathematics 2025-04-01 Emil Graf , Alex Townsend

Let $\Omega$ be a bounded domain in $\mathbb R^2$ with smooth boundary $\partial\Omega$, and let $\omega_h$ be the set of points in $\Omega$ whose distance from the boundary is smaller than $h$. We prove that the eigenvalues of the…

Spectral Theory · Mathematics 2022-11-01 Francesco Ferraresso , Luigi Provenzano

In this paper we are concerned with convergence of solutions of the Poisson equation with Neumann boundary conditions in a two-dimensional thin domain exhibiting highly oscillatory behavior in part of its boundary. We deal with the resonant…

Analysis of PDEs · Mathematics 2013-11-14 Marcone C. Pereira , Ricardo P. Silva

We study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half space. The aim is to solve boundary value problems with boundary data of negative regularity and to describe the…

Analysis of PDEs · Mathematics 2021-05-27 Felix Hummel

We consider the problem of numerically approximating the solutions to a partial differential equation (PDE) when there is insufficient information to determine a unique solution. Our main example is the Poisson boundary value problem, when…

Numerical Analysis · Mathematics 2023-12-21 Peter Binev , Andrea Bonito , Albert Cohen , Wolfgang Dahmen , Ronald DeVore , Guergana Petrova

In this paper we propose a subgradient algorithm for solving the equilibrium problem where the bifunction may be quasiconvex with respect to the second variable. The convergence of the algorithm is investigated. A numerical example for a…

Optimization and Control · Mathematics 2019-11-04 Le Hai Yen , Le Dung Muu

Let $\om $ be a bounded domain in an $n$-dimensional Euclidean space $\Bbb R^n$. We study eigenvalues of an eigenvalue problem of a system of elliptic equations: $$ \{\aligned &\Delta {\mathbf u}+ \alpha{\rm grad}(\text{div}{\mathbf…

Differential Geometry · Mathematics 2010-09-09 Daguang Chen , Qing-Ming Cheng , Qiaoling Wang , Changyu Xia

In this paper, we discuss approximating the eigenvalue problem of biharmonic equation. We first present an equivalent mixed formulation which admits amiable nested discretization. Then, we construct multi-level finite element schemes by…

Numerical Analysis · Mathematics 2016-06-20 Shuo Zhang , Yingxia Xi , Xia Ji

This paper considers the finite element solution of the boundary value problem of Poisson's equation and proposes a guaranteed em a posteriori local error estimation based on the hypercircle method. Compared to the existing literature on…

Numerical Analysis · Mathematics 2021-12-17 Taiga Nakano , Xuefeng Liu

This paper presents a mixed basis approach for Laplace eigenvalue problems, which treats the boundary as a perturbation of the free Laplace operator. The method separates the boundary from the volume via a generic function that can be…

Chemical Physics · Physics 2009-09-07 Matias Nordin , Martin Nilsson-Jacobi , Magnus Nydén

We design a variational quantum algorithm to solve multi-dimensional Poisson equations with mixed boundary conditions that are typically required in various fields of computational science. Employing an objective function that is formulated…

Quantum Physics · Physics 2025-05-26 Minjin Choi , Hoon Ryu

A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…

Other Computer Science · Computer Science 2015-05-28 Nelly Pustelnik , Jean-Christophe Pesquet , Caroline Chaux

We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convexified version of the problem, in which…

Optimization and Control · Mathematics 2016-01-12 Madeleine Udell , Stephen Boyd

A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of…

Optimization and Control · Mathematics 2009-11-13 Patrick L. Combettes , Jean-Christophe Pesquet

In this paper we study eigenvalues of Laplacian and biharmonic operators on compact domains in complete manifolds. We establish several new inequalities for eigenvalues of Laplacian and biharmonic operators respectively by using Sobolev…

Differential Geometry · Mathematics 2024-12-23 Yong Luo , Xianjing Zheng

This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial…

Optimization and Control · Mathematics 2017-05-30 Jinyan Fan , Jiawang Nie , Anwa Zhou

We consider an elliptic polyharmonic problem of any order which takes place in a punctured bounded domain with Navier conditions. We prove that if the domain is convex in one direction and symmetric with respect to the reflections induced…

Analysis of PDEs · Mathematics 2018-10-08 Stefano Biagi , Enrico Valdinoci , Eugenio Vecchi