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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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|
|Depositing User:||Dr. David A. Cumming|
|Date Deposited:||01 Oct 2008 16:50|
|Last Modified:||12 Jan 2011 04:49|
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