Research Output

On the algebraic foundations of the vector epsilon-algorithm.

  We review the Clifford algebraic foundations of versions of the vector epsilon-algorithm. This involves the formation of rational approximants to vector-valued functions defined by a power series. We summarise their properties and demonstrate how a study of these algebraic constructs leads to convergence results concerning the vector epsilon-table which we apply to the iterative solution of simultaneous linear equations. The generalisation of the epsilon-algorithm to vector rational Hermite interpolants is also presented. Finally, we consider various algebraic representations for generalised inverse rational approximants and interpolants.

  • Type:

    Book Chapter

  • Date:

    31 January 1995

  • Publication Status:

    Published

  • Publisher

    Kluwer Academic

  • Library of Congress:

    QA Mathematics

  • Dewey Decimal Classification:

    512 Algebra

Citation

Roberts, D. E. (1995). On the algebraic foundations of the vector epsilon-algorithm. In Ablamowicz, R. & Lounesto, P. (Eds.). Clifford algebras and spinor structures: A special volume dedicated to the memory of Albert Crumeyrolle (1919-1992)., 343-361. Kluwer Academic. ISBN 0792333667 or 9780792333661

Keywords

Vector epsilon-algorithm; Vector rational approximants; Hermite interpolants; Iterative solutions; Linear equations.

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