  We develop a toolbox for the error analysis of linear recurrences with
constant or polynomial coefficients, based on generating series, Cauchy's
method of majorants, and simple results from analytic combinatorics. We
illustrate the power of the approach by several nontrivial application
examples. Among these examples are a new worst-case analysis of an algorithm
for computing Bernoulli numbers, and a new algorithm for evaluating
differentially finite functions in interval arithmetic while avoiding interval
blow-up.
