Convergence of Arnoldi’s method for generalized eigenvalue problems
Version: 1,
Uploaded by: Administrator,
Date Uploaded:
26 November 2022
Warning
You are about to be redirected to a website not operated by the Mauritius Research and Innovation Council. Kindly note that we are not responsible for the availability or content of the linked site. Are you sure you want to leave this page?
By constructing a-posteriori residual bounds, this paper consider the convergence of implicitly restarted Arnoldi’s methods for generalized eigenvalue problems. Such bounds have been less studied in comparison to bounds on the angle between an eigenvector and the Krylov subspace. Numerical validations of the bounds are given and both cases of convergence and non-convergence are illustrated for the shift-and-invert Arnoldi method and its refined variant. Alternative stopping criteria are also proposed for the Arnoldi methods.