Related papers: Rectangular eigenvalue problems
We discuss the approximation of the eigensolutions associated with the Maxwell eigenvalues problem in the framework of least-squares finite elements. We write the Maxwell curl curl equation as a system of two first order equation and design…
In this paper, we develop regularized discrete least squares collocation and finite volume methods for solving two-dimensional nonlinear time-dependent partial differential equations on irregular domains. The solution is approximated using…
We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity…
Given a random quantum state of multiple distinguishable or indistinguishable particles, we provide an effective method, rooted in symplectic geometry, to compute the joint probability distribution of the eigenvalues of its one-body reduced…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form $\m{A}x=\lambda\m{B}x$, where the matrices $\m{A}$ and/or $\m{B}$ may depend on a scalar parameter.…
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…
We consider the problem of partitioning the node set of a graph into $k$ sets of given sizes in order to \emph{minimize the cut} obtained using (removing) the $k$-th set. If the resulting cut has value $0$, then we have obtained a vertex…
In this paper we analyze and solve eigenvalue programs, which consist of the task of minimizing a function subject to constraints on the "eigenvalues" of the decision variable. Here, by making use of the FTvN systems framework introduced by…
Quartic eigenvalue problem $(\lambda^4 A + \lambda^3 B + \lambda^2C + \lambda D + E)x = \mathbf{0}$ naturally arises e.g. when solving the Orr-Sommerfeld equation in the analysis of the stability of the {Poiseuille} flow, in theoretical…
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…
We examine some numerical iterative methods for computing the eigenvalues and eigenvectors of real matrices. The five methods examined here range from the simple power iteration method to the more complicated QR iteration method. The…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
Quantum subspace diagonalization methods are an exciting new class of algorithms for solving large\rev{-}scale eigenvalue problems using quantum computers. Unfortunately, these methods require the solution of an ill-conditioned generalized…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature problems that may…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
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 introduce a Generalized Randomized QR-decomposition that may be applied to arbitrary products of matrices and their inverses, without needing to explicitly compute the products or inverses. This factorization is a critical part of a…
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…