Sylvester-Habicht Sequences and Fast Cauchy Index Computation

摘要

In this paper we show how Schonhage's strategy for computing continued fractions Schonhage (1971) can be combined with the theory of sub-resultants (Habicht, 1948; Collins, 1967; Brown, 1971; Brown and Traub, 1971; Loos, 1982; Gonzalez et al., 1990, 1994; Ducos, 1996; Ho and Yap, 1996; Lazard, 1998; Quitte, 1998) in order to compute the Cauchy index of a rational function or the signature of a non-singular Hankel matrix in a fast and also storage efficient way.