  We develop algorithms for certifying an approximation to a nonsingular
solution of a square system of equations built from univariate analytic
functions. These algorithms are based on the existence of oracles for
evaluating basic data about the input analytic functions. One approach for
certification is based on alpha-theory while the other is based on the Krawczyk
generalization of Newton's iteration. We show that the necessary oracles exist
for D-finite functions and compare the two algorithmic approaches for this case
using our software implementation in SageMath.
