Solvers for large sparse linear systems come in two categories: direct and iterative.
Amesos2, a package in the Trilinos software project, provides direct methods, and Belos …

We introduce the generalized preconditioned locally harmonic residual (GPLHR) method for
solving standard and generalized non-Hermitian eigenproblems. The method is particularly …

Certain applications that analyze dam** effects require the solution of quadratic
eigenvalue problems (QEPs). We use refined isogeometric analysis (rIGA) to solve quadratic …

This thesis studies the so-called “criticality problem”, an important generalised eigenvalue
problem arising in neutron transport theory. The smallest positive real eigenvalue of the …

The FEAST eigenvalue algorithm is a subspace iteration algorithm that uses contour
integration to obtain the eigenvectors of a matrix for the eigenvalues that are located in any …

This work focus on the iterative solution of large linear systems with multiple right-hand
sidesthat appear in various scientific applications. When multiple right-hand sides have to …

We study inexact Rayleigh quotient iteration (IRQI) for computing a simple interior eigenpair
of the generalized eigenvalue problem Av= λ Bv, providing new insights into a special type …

High fidelity simulation of nuclear reactors entails large scale applications characterized with
high dimensionality and tremendous complexity where various physics models are …

We study an inexact implicitly restarted Arnoldi (IRA) method for computing a few eigenpairs
of generalized non-Hermitian eigenvalue problems with spectral transformation, where in …

In this paper, we present a new type of restarted Krylov method for calculating the smallest
eigenvalues of a symmetric positive definite matrix G. The new framework avoids the …