On ε approximations of persistence diagrams

Jonathan Jaquette, Miroslav Kramár

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1887-1912
Number of pages26
JournalMathematics of Computation
Issue number306
StatePublished - 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics


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