David W. Jacobs, Daphna Weinshall, et al.
IEEE Transactions on Pattern Analysis and Machine Intelligence
We present theoretical and numerical comparisons between Arnoldi and nonsymmetric Lanczos procedures for computing eigenvalues of nonsymmetric matrices. In exact arithmetic we prove that any type of eigenvalue convergence behavior obtained using a nonsymmetric Lanczos procedure may also be obtained using an Arnoldi procedure but on a different matrix and with a different starting vector. In exact arithmetic we derive relationships between these types of procedures and normal matrices which suggest some interesting questions regarding the roles of nonnormality and of the choice of starting vectors in any characterizations of the convergence behavior of these procedures. Then, through a set of numerical experiments on a complex Arnoldi and on a complex nonsymmetric Lanczos procedure, we consider the more practical question of the behavior of these procedures when they are applied to the same matrices.
David W. Jacobs, Daphna Weinshall, et al.
IEEE Transactions on Pattern Analysis and Machine Intelligence
Sonia Cafieri, Jon Lee, et al.
Journal of Global Optimization
Nimrod Megiddo
Journal of Symbolic Computation
John R. Kender, Rick Kjeldsen
IEEE Transactions on Pattern Analysis and Machine Intelligence