We describe new algorithms of the locally optimal block preconditioned conjugate gradient
(LOBPCG) method for symmetric eigenvalue problems, based on a local optimization of a …

This article describes the PRIMME software package for solving large, sparse Hermitian
standard eigenvalue problems. The difficulty and importance of these problems have …

A new software code for computing selected eigenvalues and associated eigenvectors of a
real symmetric matrix is described. The eigenvalues are either the smallest or those closest …

In two previous papers by Neymeyr [Linear Algebra Appl. 322 (1–3)(2001) 61; 322 (1–
3)(2001) 87], a sharp, but cumbersome, convergence rate estimate was proved for a simple …

The goal of our paper is to compare a number of algorithms for computing a large number of
eigenvectors of the generalized symmetric eigenvalue problem arising from a modal …

This document is a survey of freely available software tools for the numerical solution of
large sparse eigenvalue problems. It includes a list of libraries, programs or subroutines …

We present a short survey of multigrid–based solvers for symmetric eigenvalue problems.
We concentrate our attention on “off the shelf” and “black box” methods, which should allow …

A polynomial filtered Davidson-type algorithm is proposed for symmetric eigenproblems, in
which the correction-equation of the Davidson approach is replaced by a polynomial filtering …

Large, sparse, Hermitian eigenvalue problems are still some of the most computationally
challenging tasks. Despite the need for a robust, nearly optimal preconditioned iterative …

Abstract CG, MINRES, and SYMMLQ are Krylov subspace methods for solving large
symmetric systems of linear equations. CG (the conjugate-gradient method) is reliable on …