Related papers: Fast randomized non-Hermitian eigensolver based on…
Rational filter functions can be used to improve convergence of contour-based eigensolvers, a popular family of algorithms for the solution of the interior eigenvalue problem. We present a framework for the optimization of rational filters…
This paper proposes an efficient method for computing selected generalized eigenpairs of a sparse Hermitian definite matrix pencil $(A,B)$. Based on Zolotarev's best rational function approximations of the signum function and conformal…
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…
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…
Calculating portions of eigenvalues and eigenvectors of matrices or matrix pencils has many applications. An approach to this calculation for Hermitian problems based on a density matrix has been proposed in 2009 and a software package…
Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often an…
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…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…
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…
Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…
This paper introduces a method for computing eigenvalues and eigenvectors of a generalized Hermitian, matrix eigenvalue problem. The work is focused on large scale eigenvalue problems, where the application of a direct inverse is out of…
A detailed new upgrade of the FEAST eigensolver targeting non-Hermitian eigenvalue problems is presented and thoroughly discussed. It aims at broadening the class of eigenproblems that can be addressed within the framework of the FEAST…
In recent years, contour-based eigensolvers have emerged as a standard approach for the solution of large and sparse eigenvalue problems. Building upon recent performance improvements through non-linear least square optimization of…
Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…
This paper presents a definition for local linearizations of rational matrices and studies their properties. This definition allows us to introduce matrix pencils associated to a rational matrix that preserve its structure of zeros and…
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 efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…
A new algorithm, denoted by RSRR, is presented for solving large-scale nonlinear eigenvalue problems (NEPs) with a focus on improving the robustness and reliability of the solution, which is a challenging task in computational science and…
Non-Hermitian operators naturally arise in the description of open quantum systems, which exhibit features such as resonances and decay processes, where the associated eigenvalues are complex. Standard quantum algorithms, including the…
Non-smoothness at optimal points is a common phenomenon in many eigenvalue optimization problems. We consider two recent algorithms to minimize the largest eigenvalue of a Hermitian matrix dependent on one parameter, both proven to be…