A Schur complement approach to a general extrapolation algorithm (Q1399251)

The authors use Schur complements and their properties to obtain various interpretations of the E-transformation. It is proved that ratios of determinants similar to those appearing in the E-transformation can be recursively computed by a triangular recursive scheme and that, reciprocally, quantities computed by such a scheme can be expressed as a ratio of determinants. Such a theory applies, in particular, to B-splines, Bernstein polynomials, orthogonal polynomials, Padé approximants, generalized divided differences, and projection methods. Thus, following the results of this paper, these items can also be interpreted as Schur complements. This approach can be extended to the vector case, thus leading to new vector sequence transformations.