Vector Continued Fraction Algorithms

D. E. Roberts ()
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D. E. Roberts: Napier University, Department of Mathematics

A chapter in Clifford Algebras with Numeric and Symbolic Computations, 1996, pp 111-119 from Springer

Abstract: Abstract We consider the construction of rational approximations to given power series whose coefficients are vectors. The approximants are in the form of vector-valued continued fractions which may be used to obtain vector Padé approximants using recurrence relations. Algorithms for the determination of the vector elements of these fractions have been established using Clifford algebras. We devise new algorithms based on these which involve operations on vectors and scalars only — a desirable characteristic for computations involving vectors of large dimension. As a consequence, we are able to form new expressions for the numerator and denominator polynomials of these approximants as products of vectors, thus retaining their Clifford nature.

Keywords: Rational approximants; vector-valued functions; continued fractions; Viskovatov; modified Euclidean algorithm; Clifford algebra (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-8157-4_7

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DOI: 10.1007/978-1-4615-8157-4_7

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