Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
SIAM Journal on Matrix Analysis and Applications
The symmetric eigenvalue problem
The symmetric eigenvalue problem
ACM Transactions on Mathematical Software (TOMS)
Low-Rank Matrix Approximation Using the Lanczos Bidiagonalization Process with Applications
SIAM Journal on Scientific Computing
Which Eigenvalues Are Found by the Lanczos Method?
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
Computing smallest singular triplets with implicitly restarted Lanczos bidiagonalization
Applied Numerical Mathematics - Numerical algorithms, parallelism and applications
Augmented Implicitly Restarted Lanczos Bidiagonalization Methods
SIAM Journal on Scientific Computing
On the Convergence of Rational Ritz Values
SIAM Journal on Matrix Analysis and Applications
| Hi-index | 7.29 |
E. Kokiopoulou et al. developed an implicitly restarted Lanczos bidiagonalization method (named IRLANB) for computing the smallest singular triplets. They use the wanted harmonic Ritz values and the corresponding refined harmonic Ritz vectors to approximate the desired smallest singular triplets. However, they use the unwanted harmonic Ritz values as shifts, named the harmonic shifts, to implicitly restart their algorithm. Therefore, although they replace the harmonic Ritz vectors by the refined harmonic Ritz vectors, which are always better than the harmonic Ritz vectors, to improve the convergence of IRLANB, the subspace after implicitly restarting is the same as that without this replacement. In this paper, using the information of the refined harmonic Ritz vectors, we present a new shift strategy, named the refined harmonic shifts, to replace the harmonic shifts used in IRLANB and obtain a new method, called IRRLANB. The refined harmonic shifts are better than the harmonic shifts and can be computed cheaply and reliably. The numerical experiments are reported to indicate that IRRLANB is superior than IRLANB.