Large-scale complex eigenvalue problems
Journal of Computational Physics
Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
Derivatives of eigenvalues and eigenvectors of matrix functions
SIAM Journal on Matrix Analysis and Applications
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
SIAM Journal on Matrix Analysis and Applications
An analysis of the Rayleigh—Ritz method for approximating eigenspaces
Mathematics of Computation
Convergence of Restarted Krylov Subspaces to Invariant Subspaces
SIAM Journal on Matrix Analysis and Applications
| Hi-index | 7.29 |
Based on Rayleigh-Ritz procedure, a new method is proposed for a few eigenpair partial derivatives of large matrices. This method simultaneously computes the approximate eigenpairs and their partial derivatives. The linear systems of equations that are solved for eigenvector partial derivatives are greatly reduced from the original matrix size. And the left eigenvectors are not required. Moreover, errors of the computed eigenpairs and their partial derivatives are investigated. Hausdorff distance and containment gap are used to measure the accuracy of approximate eigenpair partial derivatives. Error bounds on the computed eigenpairs and their partial derivatives are derived. Finally numerical experiments are reported to show the efficiency of the proposed method.