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

| PDF (Contains mathematical notation) Available under License Creative Commons Attribution Non-commercial No Derivatives. Download (201kB) | Preview |

## 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: | 02 Jun 2014 16:43 |

URI: | http://researchrepository.napier.ac.uk/id/eprint/2424 |

### Actions (login required)

View Item |