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Dept. of Mathematics and Computer Science (Berlin)

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reviewer: M. Znojil

reviewernum: 9689

revieweremail: znojil@ujf.cas.cz

zblno: DE015329997

author: Luk, Franklin T.; Qiao, Sanzheng:

shorttitle: A fast algorithm for Hankel matrices

source: Lin. Algebra Appl. 316, No. 1-3, 171-182 (2000)

rpclass: 65F15

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.

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