  We explore a novel application of zero-dimensional persistent homology from
Topological Data Analysis (TDA) for bracketing zero-crossings of both
one-dimensional continuous functions, and uniformly sampled time series. We
present an algorithm and show its robustness in the presence of noise for a
range of sampling frequencies. In comparison to state-of-the-art software-based
methods for finding zeros of a time series, our method generally converges
faster, provides higher accuracy, and is capable of finding all the roots in a
given interval instead of converging only to one of them. We also present and
compare options for automatically setting the persistence threshold parameter
that influences the accurate bracketing of the roots.
