On a representation of vector continued fractions

摘要

Vector Padé approximants to power series with vector coefficients may be calculated using the three-term recurrence relations of vector continued fractions if formulated in the framework of Clifford algebras. We show that the numerator and denominator polynomials of these fractions take particularly simple forms which require just a few degrees of freedom in their representation. The new description also allows the calculation of “hybrid” approximants.