INSPIRING FUTURES

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

[img]
Preview
PDF
Available under License Creative Commons Attribution Non-commercial No Derivatives.

Download (219kB) | Preview

    Abstract/Description

    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 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: Dr. David A. Cumming
    Date Deposited: 01 Oct 2008 19:53
    Last Modified: 18 Sep 2013 13:56
    URI: http://researchrepository.napier.ac.uk/id/eprint/2426

    Actions (login required)

    View Item

    Document Downloads

    More statistics for this item...

    Edinburgh Napier University is a registered Scottish charity. Registration number SC018373