On the algebraic foundations of the vector epsilon-algorithm.

Roberts, David E

Abstract

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.

Citation

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

• Publication Date: 1995-02
• Deposit Date: Oct 1, 2008
• Publicly Available Date: Oct 1, 2008
• Peer Reviewed: Peer Reviewed
• Pages: 343-361
• Book Title: Clifford algebras and spinor structures: A special volume dedicated to the memory of Albert Crumeyrolle (1919-1992).
• ISBN: 0792333667 or 9780792333661
• Keywords: Vector epsilon-algorithm; Vector rational approximants; Hermite interpolants; Iterative solutions; Linear equations.
• Public URL: http://researchrepository.napier.ac.uk/id/eprint/2424
• Contract Date: Oct 1, 2008