A fast eigenvalue algorithm for Hankel matrices (Q1587283)

A pioneering transfer of experience from the real symmetric matrices to their complex symmetric counterparts. NB: The idea could find a broad applicability [cf. PT symmetric quantum mechanics models in \textit{F. M. Fernandez, R. Guardiola, J. Ros}, and \textit{M. Znojil}, J. Phys. A: Math. Gen. 31, No. 50, 10105-10112 (1998) for a sample]. For Hankel matrices of this type the authors develop a fast algorithm for the determination of all the eigenvalues. Starting from the concept of a complex orthogonality and from a fast Hankel-vector multiplication the paper suggests a combination of the Lanczos tridiagonalization with QR diagonalization. Numerical illustrations are encouraging. Several theoretical questions (cf. the loss of the complex-orthogonality of the Lanczos vectors) remain open.