GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
SIAM Journal on Matrix Analysis and Applications
The trace minimization method for the symmetric generalized eigenvalue problem
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
SIAM Journal on Scientific Computing
A Krylov--Schur Algorithm for Large Eigenproblems
SIAM Journal on Matrix Analysis and Applications
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Anasazi software for the numerical solution of large-scale eigenvalue problems
ACM Transactions on Mathematical Software (TOMS)
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Eigenvalue problems arise in many computational science and engineering applications: in structural mechanics, nanoelectronics, and Google's PageRank link analysis, for example. Often, the large size of these eigenvalue problems requires the development of eigensolvers that scale well on parallel computing platforms. In this paper, we compare the effectiveness and robustness of our eigensolver for the symmetric generalized eigenvalue problem, the trace minimization scheme TraceMIN-developed in the early 1980s-against today's well-known sparse eigensolvers including: the LOBPCG and block Krylov-Schur implementations in Trilinos; ARPACK; and several methods in the PRIMME package such as the Jacobi-Davidson one. In addition, we demonstrate the parallel scalability of two variants of TraceMIN on multicore nodes as well as on large clusters of such nodes. Our results show that TraceMIN is more robust and has higher parallel scalability than the above-mentioned competing eigensolvers.