2014/12/04 by Jaquette, Jonathan, Kramár, Miroslav
#55-04 #55N99 #Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1412.1805
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently observed in nature. In this paper a theoretical framework for the algorithmic computation of an arbitrarily good approximation of the persistent homology is developed. We study the filtrations generated by sub-level sets of a function f : X → ℝ, where X is a CW-complex. In the special case X = [0,1]N, N ∈ ℕ we discuss implementation of the proposed algorithms. We also investigate a priori and a posteriori bounds of the approximation error introduced by our method.