Roberts, David E (1998) *On a vector q-d algorithm.* Advances in Computational Mathematics, 8 (3). pp. 193-219. ISSN 1019 7168

| 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 |