ACM Transactions on Mathematical Software (TOMS)
Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
Quasi-kernel polynomials and their use in non-Hermitian matrix iterations
Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
The Convergence of Generalized Lanczos Methods for Large Unsymmetric Eigenproblems
SIAM Journal on Matrix Analysis and Applications
A refined subspace iteration algorithm for large sparse eigenproblems
Applied Numerical Mathematics
Implicitly Restarted GMRES and Arnoldi Methods for Nonsymmetric Systems of Equations
SIAM Journal on Matrix Analysis and Applications
An analysis of the Rayleigh—Ritz method for approximating eigenspaces
Mathematics of Computation
A refined jacobi-davidson method and its correction equation
Computers & Mathematics with Applications
| Hi-index | 0.98 |
The work is fourfold. First, a refined harmonic Rayleigh-Ritz procedure is proposed, some relationships are established between the refined harmonic Ritz vector and the harmonic Ritz vector, an a priori error bound is derived for the refined harmonic Ritz vector, and some properties are established on Rayleigh quotients and residual norms. Second, a resulting refined harmonic Arnoldi method is discussed, and how to compute the refined harmonic Ritz vectors cheaply and accurately is considered. Third, an explicitly restarted refined harmonic Arnoldi algorithm is developed over an augmented Krylov subspace. Finally, numerical examples are reported that compare the new algorithm with the implicitly restarted harmonic Arnoldi algorithm (IRHA) and the implicitly restarted refined harmonic Arnoldi algorithm (IRRHA). Numerical results confirm efficiency of the new algorithm.