Vector Padé-type approximants and vector Padé approximants
The theory of scalar Padé and Padé-type approximants is generalized to the vector case. Like in \textit{A. Salam} [Adv. Comput. Math. 8, No. 3, 267-289 (1998; Zbl 0906.42013)] Clifford algebra techniques are used that differ however from those used in \textit{D. E. Roberts} [Clifford algebras and vector-valued rational forms. I: Proc. R. Soc. Lond., Ser. A 431, No. 1882, 285-300 (1990; Zbl 0745.41017); II: Numer. Algorithms 3, No. 1-4, 371-381 (1992; Zbl 0782.41022)]. The relation between both, and the link with the generalized inverse Padé approximants of \textit{P. Graves-Morris} [Vector valued interpolants I: Numer. Math. 42, 331-348 (1983; Zbl 0525.41014); II: IMA J. Numer. Anal. 4, 209-224 (1984; Zbl 0558.41019)] and \textit{P. Graves-Morris} and \textit{C. D. Jenkins} [III: Constructive Approximation 2, 263-289 (1986; Zbl 0614.41016)] is given. The derivation relies on the vector orthogonal polynomials developed by the author in the paper mentioned. Thanks to the Clifford algebra techniques direct generalizations of scalar results, including a \(qd\)-algorithm and continued fractions are obtained.
scientific article; zbMATH DE number 1286391
scientific article