author: Luk, Franklin T.; Qiao, Sanzheng:
shorttitle: A fast algorithm for Hankel matrices
source: Lin. Algebra Appl. 316, No. 1-3, 171-182 (2000)
rsclass: 15A23; 65T50
keywords: Hankel complex matrices; Lanczos tridiagonalization; complex orthogonal transformation; eigenvalues
revtext: A pioneering transfer of experience from the real symetric matrices to their complex symmetric counterparts. NB: The idea could find a broad applicability (cf. PT symmetric quantum mechanics models in F. M. Fernandez et al, J. Phys. A: Math. Gen. 31 (1998) 10105 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.