An iterative block Arnoldi algorithm with modified approximate eigenvectors for large unsymmetric eigenvalue problems
In order to handle large unsymmetric eigenvalue problems the author modifies the \(m\)-step Arnoldi method to its block version. The resulting algorithm updates the block Krylov subspaces \(K_{m}\left( A,V_{1}\right) ,\) spanned by \(V_{1},AV_{1},\dots,AV_{1}^{m-1},\) where \(V_{1}\) is an initial \(N\times p\) orthonormal matrix. It basically uses the Ritz pair \(\left( \lambda _{i}^{(m)},\varphi _{i}^{(m)}\right) \;\)of \(A\) in \(K_{m}\left( A,V_{1}\right) \) to approximate the sought eigenpair \(\left( \lambda _{i},\varphi _{i}\right).\) The two main advantages of the method are: its efficiency to compute clustered eigenvalues and also multiple eigenvalues. The algorithm is also suitable for parallel processing. The convergence of the method is examined and numerical experiments are used to illustrate the efficiency of the method.
scientific article; zbMATH DE number 2082102