Related papers: Solving singular generalized eigenvalue problems b…

We study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data. With the stochastic Galerkin approach, the solutions are represented as…

For the computation of the generalized singular value decomposition (GSVD) of a large matrix pair $(A,B)$ of full column rank, the GSVD is commonly formulated as two mathematically equivalent generalized eigenvalue problems, so that a…

Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…

The first step when solving an infinite-dimensional eigenvalue problem is often to discretize it. We show that one must be extremely careful when discretizing nonlinear eigenvalue problems. Using examples, we show that discretization can:…

A fast implicit QR algorithm for eigenvalue computation of low rank corrections of unitary matrices is adjusted to work with matrix pencils arising from polynomial zerofinding problems . The modified QZ algorithm computes the generalized…

The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…

The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…

In this paper, numerical solutions of singularly perturbed boundary value problems are given by using variants of finite element method. Both Galerkin and subdomain Galerkin method based on quadratic B-spline functions are applied over the…

The eigenproblem of low-rank updated matrices are of crucial importance in many applications. Recently, an upper bound on the number of distinct eigenvalues of a perturbed matrix was established. The result can be applied to estimate the…

We describe a novel algorithm for solving general parametric (nonlinear) eigenvalue problems. Our method has two steps: first, high-accuracy solutions of non-parametric versions of the problem are gathered at some values of the parameters;…

We investigate the eigengenvalues problem for self-adjoint operators with the singular perturbations. The general results presented here includes weakly as well as strongly singular cases. We illustrate these results on two models which…

Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…

In this article, we study the singular case of an homogeneous generalized discrete time system with given initial conditions. We consider the matrix pencil singular and provide necessary and sufficient conditions for existence and…

The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…

We propose a verified computation method for partial eigenvalues of a Hermitian generalized eigenproblem. The block Sakurai-Sugiura Hankel method, a contour integral-type eigensolver, can reduce a given eigenproblem into a generalized…

We describe two algorithms for the eigenvalue, eigenvector problem which, on input a Gaussian matrix with complex entries, finish with probability 1 and in average polynomial time.

Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some…

Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Iterative random sparsification methods allow for the estimation of a single dominant eigenvalue at reduced cost by…

In this paper, a full (nested) multigrid scheme is proposed to solve eigenvalue problems. The idea here is to use the multilevel correction method to transform the solution of eigenvalue problem to a series of solutions of the corresponding…

The rectangular multiparameter eigenvalue problem (RMEP) involves rectangular coefficient matrices (usually with more rows than columns) and may potentially have no solution in its original form. A minimal perturbation framework is proposed…