On a vector q-d algorithm.

Roberts, David E (1998) On a vector q-d algorithm. Advances in Computational Mathematics, 8 (3). pp. 193-219. ISSN 1019 7168

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Using the framework provided by Clifford algebras, we consider a noncommutative quotient-difference algorithm for obtaining the elements of a continued fraction corresponding to a given vector-valued power series. We
demonstrate that these elements are ratios of vectors, which may be calculated with the aid of a cross rule using only vector operations. For vector-valued meromorphic functions we derive the asymptotic behaviour of these vectors, and hence of the continued fraction elements themselves. The behaviour of these elements is similar to that in the scalar case, while the vectors are
linked with the residues of the given function. In the particular case of vector power series arising from matrix iteration the new algorithm amounts to a
generalisation of the power method to sub-dominant eigenvalues, and their eigenvectors.

Item Type: Article
Print ISSN: 1019 7168
Electronic ISSN: 1572 9044
Additional Information: The original publication is available at
Uncontrolled Keywords: Vector continued fraction; Vector Pad´e approximant; Quotientdifference algorithm; Clifford algebra; Cross rule; Power method.
University Divisions/Research Centres: Faculty of Engineering, Computing and Creative Industries > School of Engineering and the Built Environment
Dewey Decimal Subjects: 500 Science > 510 Mathematics > 512 Algebra
Library of Congress Subjects: Q Science > QA Mathematics
Item ID: 2426
Depositing User: Users 10 not found.
Date Deposited: 01 Oct 2008 18:53
Last Modified: 18 Sep 2013 12:56

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