Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
Analysis and implementation of an implicitly restarted Arnoldi iteration
Analysis and implementation of an implicitly restarted Arnoldi iteration
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Matrix algorithms
| Hi-index | 0.09 |
It is generally believed that the Ritz vectors do not coincide with the refined Ritz vectors in the Arnoldi method for computing eigenvalues of matrices. We show that this coincidence is theoretically possible. We provide a necessary and sufficient condition for this coincidence to happen and give examples to illustrate the same. Using Lanczos polynomials, we give a polynomial characterization of refined Ritz vectors of symmetric matrices that is different from the one available in the literature.