On ε approximations of persistence diagrams

Jonathan Jaquette, Miroslav Kramár

    研究成果: Article査読

    1 被引用数 (Scopus)

    抄録

    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.

    本文言語English
    ページ(範囲)1887-1912
    ページ数26
    ジャーナルMathematics of Computation
    86
    306
    DOI
    出版ステータスPublished - 2017

    ASJC Scopus subject areas

    • 代数と数論
    • 計算数学
    • 応用数学

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