Roberts, David E (1998) On a vector qd algorithm. Advances in Computational Mathematics, 8 (3). pp. 193219. ISSN 1019 7168

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Abstract/Description
Using the framework provided by Clifford algebras, we consider a noncommutative quotientdifference algorithm for obtaining the elements of a continued fraction corresponding to a given vectorvalued 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 vectorvalued 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 subdominant eigenvalues, and their eigenvectors.
Item Type:  Article 

Print ISSN:  1019 7168 
Electronic ISSN:  1572 9044 
Additional Information:  The original publication is available at http://www.springerlink.com 
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 
URI:  http://researchrepository.napier.ac.uk/id/eprint/2426 
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