Chebyshev acceleration techniques for large complex non Hermitian eigenvalue problems (Q1916981)

It is proposed that eigenvalues of a large non-Hermitian matrix are computed by first applying an \(r^*r\) block Arnoldi algorithm, and then using the computed Ritz values to determine an ellipse that has those eigenvalues sought on its outside. Then this ellipse is used to determine a Chebyshev acceleration that is applied to the \(r\) leading Ritz vectors obtained from Arnoldi. The technique is tested on 2 applied problems, an Orr-Sommerfeld operator and one of the test matrices from the Harwell-Boeing collection.