A harmonic restarted Arnoldi algorithm for calculating eigenvalues and determining multiplicity
By Ronald B. Morgan, Min-Li Zeng. 2006
71 citations recorded by the source corpus.
Abstract A restarted Arnoldi algorithm is given that computes eigenvalues and eigenvectors. It is related to implicitly restarted Arnoldi, but has a simpler restarting approach. Harmonic and regular Rayleigh–Ritz versions are possible. For multiple eigenvalues, an approach is proposed that first computes eigenvalues with the new harmonic restarted Arnoldi algorithm, then uses random restarts to determine multiplicity. This avoids the need for a block method or for relying on roundoff error to produce the multiple copies.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/02fbc5c4b2f5f245dea9beff98f956cc1561e967
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Augmented Implicitly Restarted Lanczos Bidiagonalization Methods (2005, background): “Morgan and Zeng [26] recently pointed out that the residual errors associated with different harmonic Ritz pairs { ˆ θ j , ˆ v j } are parallel.”