Related papers: A quadrature-based eigensolver with a Krylov subsp…
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…
In this paper we develop randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems. Building on the recently developed randomized Gram-Schmidt process, where sketched inner…
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…
The Conjugate Gradient method (CGM) is known to be the fastest generic iterative method for solving linear systems with symmetric sign definite matrices. In this paper, we modify this method so that it could find fundamental solitary waves…
This paper is concerned with the nonnegative inverse eigenvalue problem of finding a nonnegative matrix such that its spectrum is the prescribed self-conjugate set of complex numbers. We first reformulate the nonnegative inverse eigenvalue…
The Helmholtz equation is related to seismic exploration, sonar, antennas, and medical imaging applications. It is one of the most challenging problems to solve in terms of accuracy and convergence due to the scalability issues of the…
Quantum inverse problem is defined as how to determine a local Hamiltonian from a single eigenstate? This question is valid not only in Hermitian system but also in non-Hermitian system. So far, most attempts are limited to Hermitian…
This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable…
Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…
Solving eigenproblem of the Laplacian matrix of a fully connected weighted graph has wide applications in data science, machine learning, and image processing, etc. However, this is very challenging because it involves expensive matrix…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with…
This paper proposes a combination of a hybrid CPU--GPU and a pure GPU software implementation of a direct algorithm for solving shifted linear systems $(A - \sigma I)X = B$ with large number of complex shifts $\sigma$ and multiple…
This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
We describe the GPU implementation of shifted or multimass iterative solvers for sparse linear systems of the sort encountered in lattice gauge theory. We provide a generic tool that can be used by those without GPU programming experience…
We consider the solution of complex symmetric shifted linear systems. Such systems arise in large-scale electronic structure simulations and there is a strong need for the fast solution of the systems. With the aim of solving the systems…
One of the most computationally expensive steps of the low-rank ADI method for large-scale Lyapunov equations is the solution of a shifted linear system at each iteration. We propose the use of the extended Krylov subspace method for this…
In this paper, we propose a novel, computationally efficient reduced order method to solve linear parabolic inverse source problems. Our approach provides accurate numerical solutions without relying on specific training data. The forward…
The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Nevertheless, there still exist challenging scenarios witnessing a…