Section: New Results

Asymptotic expansions for linear homogeneous divide-and-conquer recurrences: Algebraic and analytic approaches collated

Linear divide-and-conquer recurrences are a classical topic in computer science, but they are often dealt with in an offhand way. Particularly the subtle oscillations they show are usually not emphasized. After having elaborated last year a new approach to the asymptotic study of such recurrences, we provide in [7] a comparison with an older approach based on number theoretic tools as Dirichlet series and residue computation. The most striking aspect of the linear approach is the simplicity and the ease of use. Reduction to normal Jordan form, computation of a joint spectral radius, dealing with a dilatation equation are all workable with a computer-algebra system. Moreover these concepts are better known by computer scientists than those of complex analysis and analytic number theory. So there is hope that this approach will more easily gain acceptance among computer scientists.