On ε approximations of persistence diagrams

Jonathan Jaquette, Miroslav Kramár

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    Abstract

    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
    Pages (from-to)1887-1912
    Number of pages26
    JournalMathematics of Computation
    Volume86
    Issue number306
    DOIs
    Publication statusPublished - 2017

    ASJC Scopus subject areas

    • Algebra and Number Theory
    • Computational Mathematics
    • Applied Mathematics

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