Low-Rank Tensor Methods With Subspace Correction For Symmetric Eigenvalue Problems

Chattez avec Graph Search

Posez n’importe quelle question sur les cours, conférences, exercices, recherches, actualités, etc. de l’EPFL ou essayez les exemples de questions ci-dessous.

AVERTISSEMENT : Le chatbot Graph n'est pas programmé pour fournir des réponses explicites ou catégoriques à vos questions. Il transforme plutôt vos questions en demandes API qui sont distribuées aux différents services informatiques officiellement administrés par l'EPFL. Son but est uniquement de collecter et de recommander des références pertinentes à des contenus que vous pouvez explorer pour vous aider à répondre à vos questions.

Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing t ...

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...

This paper deals with the initial value problem for a semilinear wave equation on a bounded domain and solutions are required to vanish on the boundary of this domain. The essential feature of the situation considered here is that the ellipticity of the sp ...

Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine ...

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

We present outlier-free isogeometric Galerkin discretizations of eigenvalue problems related to the biharmonic and the polyharmonic operator in the univariate setting. These are Galerkin discretizations in certain spline subspaces that provide accurate app ...

The transmission eigenvalue problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. In this work, we establish the Weyl law for the eigenvalues and the completeness of the generalized eigenf ...

Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- (PT-) and anti-PT-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian sp ...

We study the homogenization of the Poisson equation with a reaction term and of the eigenvalue problem associated to the generator of multiscale Langevin dynamics. Our analysis extends the theory of two-scale convergence to the case of weighted Sobolev spa ...

We address the numerical solution of the Dirichlet problem for the two-dimensional elliptic Monge-Ampere equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators from the nonlinearitie ...

In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...

Sylvester matrix equations are ubiquitous in scientific computing. However, few solution techniques exist for their generalized multiterm version, as they now arise in an increasingly large number of applications. In this work, we consider algebraic parame ...

The mortar finite element method is a well-established method for the numerical solution of partial differential equations on domains displaying non-conforming interfaces. The method is known for its application in computational contact mechanics. However, ...

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

The parallel Schwarz method (PSM) is an overlapping domain decomposition (DD) method to solve partial differential equations (PDEs). Similarly to classical nonoverlapping DD methods, the PSM admits a substructured formulation, that is, it can be formulated ...

The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random realizations. Despite its ...

We propose the realization of exceptional points (EP) at bound states in the continuum (BIC), with two coupled strips, made of an electron-beam resist and patterned on the thin film photonic integrated platform, which makes possible etchless photonics inte ...

Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system with the mass matrix at each time step. For applications in structural dynamics, the solution of the li ...

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier–Stokes equations. Our algorithm is based on an approximated domain-decomposition of the ...

Low-Rank Tensor Methods With Subspace Correction For Symmetric Eigenvalue Problems

Chattez avec Graph Search

RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

Critical degeneracy in a nonlinear hyperbolic equation can produce atypical instability

COMMUNICATION LOWER BOUNDS AND OPTIMAL ALGORITHMS FOR MULTIPLE TENSOR-TIMES-MATRIX COMPUTATION

Low-Rank Tensor Methods for High-Dimensional Problems

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems

Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces

An Adaptive Least-squares Algorithm for the Elliptic Monge-ampere Equation

The first Grushin eigenvalue on cartesian product domains

Preconditioning techniques for generalized Sylvester matrix equations

The INTERNODES method for applications in contact mechanics and dedicated preconditioning techniques

TimeEvolver: A program for time evolution with improved error bound

Spectral Coarse Spaces for the Substructured Parallel Schwarz Method

Preconditioners for robust optimal control problems under uncertainty

Exceptional points at bound states in the continuum in photonic integrated circuits

A mathematical theory for mass lumping and its generalization with applications to isogeometric analysis

Model order reduction of flow based on a modular geometrical approximation of blood vessels