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Roberts, David E (1995) On the algebraic foundations of the vector epsilon-algorithm. In: Clifford algebras and spinor structures: A special volume dedicated to the memory of Albert Crumeyrolle (1919-1992). Mathematics and its applications (321). Kluwer Academic, pp. 343-361. ISBN 0792333667 or 9780792333661
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Abstract/Description
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.
| Item Type: | Book Section |
|---|---|
| ISBN: | 0792333667 or 9780792333661 |
| Uncontrolled Keywords: | Vector epsilon-algorithm; Vector rational approximants; Hermite interpolants; Iterative solutions; Linear equations. |
| 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: | 2424 |
| Depositing User: | Dr. David A. Cumming |
| Date Deposited: | 01 Oct 2008 16:50 |
| Last Modified: | 12 Jan 2011 04:49 |
| URI: | http://researchrepository.napier.ac.uk/id/eprint/2424 |
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