Related papers: A Krylov Eigenvalue Solver Based on Filtered Time …
This paper describes a set of rational filtering algorithms to compute a few eigenvalues (and associated eigenvectors) of non-Hermitian matrix pencils. Our interest lies in computing eigenvalues located inside a given disk, and the proposed…
Interior eigenvalue problems for large-scale sparse Hermitian matrices are fundamental in computational science. We propose an adaptive polynomial filtering strategy based on Chebyshev expansion of a step function, integrated into a…
This paper proposes a rational filtering domain decomposition technique for the solution of large and sparse symmetric generalized eigenvalue problems. The proposed technique is purely algebraic and decomposes the eigenvalue problem…
In this paper, we develop algorithms for computing the recurrence coefficients corresponding to multiple orthogonal polynomials on the step-line. We reformulate the problem as an inverse eigenvalue problem, which can be solved using…
Several problems in machine learning, statistics, and other fields rely on computing eigenvectors. For large scale problems, the computation of these eigenvectors is typically performed via iterative schemes such as subspace iteration or…
In this paper, by introducing a class of relaxed filtered Krylov subspaces, we propose the relaxed filtered Krylov subspace method for computing the eigenvalues with the largest real parts and the corresponding eigenvectors of non-symmetric…
We consider the solution of large-scale nonlinear algebraic Hermitian eigenproblems of the form $T(\lambda)v=0$ that admit a variational characterization of eigenvalues. These problems arise in a variety of applications and are…
Eigensolvers involving complex moments can determine all the eigenvalues in a given region in the complex plane and the corresponding eigenvectors of a regular linear matrix pencil. The complex moment acts as a filter for extracting…
We propose a wave operator method to calculate eigenvalues and eigenvectors of large parameter-dependent matrices, using an adaptative active subspace. We consider a hamiltonian which depends on external adjustable or adiabatic parameters,…
We propose a verified computation method for eigenvalues in a region and the corresponding eigenvectors of generalized Hermitian eigenvalue problems. The proposed method uses complex moments to extract the eigencomponents of interest from a…
An algorithm named EigenWave is described to compute eigenvalues and eigenvectors of elliptic boundary value problems. The algorithm, based on the recently developed WaveHoltz scheme, solves a related time-dependent wave equation as part of…
Consider a symmetric matrix $A(v)\in\RR^{n\times n}$ depending on a vector $v\in\RR^n$ and satisfying the property $A(\alpha v)=A(v)$ for any $\alpha\in\RR\backslash{0}$. We will here study the problem of finding $(\lambda,v)\in\RR\times…
We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane. The method uses complex integrals of the…
Recently a novel family of eigensolvers, called spectral indicator methods (SIMs), was proposed. Given a region on the complex plane, SIMs first compute an indicator by the spectral projection. The indicator is used to test if the region…
We consider a quadrature-based eigensolver to find eigenpairs of Hermitian matrices arising in lattice quantum chromodynamics. To reduce the computational cost for finding eigenpairs of such Hermitian matrices, we propose a new technique…
The eigenvector-eigenvalue identity relates the eigenvectors of a Hermitian matrix to its eigenvalues and the eigenvalues of its principal submatrices in which the jth row and column have been removed. We show that one-dimensional arrays of…
We present an iteration for the computation of simple eigenvalues using a pseudospectrum approach. The most appealing characteristic of the proposed iteration is that it reduces the computation of a single eigenvalue to a small number of…
This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…
A generalized eigenvalue algorithm for tridiagonal matrix pencils is presented. The algorithm appears as the time evolution equation of a nonautonomous discrete integrable system associated with a polynomial sequence which has some…
Contour-integral-based rational filter leads to interior eigensolvers for non-Hermitian generalized eigenvalue problems. Based on Zolotarev's third problem, this paper proves the asymptotic optimality of the trapezoidal quadrature of the…