Rigorous cubical approximation and persistent homology of continuous functions

Pawel Dlotko 1 Thomas Wanner 2
1 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions defined on finite-dimensional Euclidean spaces in such a way that the discretization error is bounded by a pre-specified small constant. While the approximation scheme has a number of potential applications, we consider its usefulness in the context of computational homology. More precisely, we demonstrate that our approximation procedure can be used to rigorously compute the persistent homology of the original continuous function on a compact domain, up to small explicitly known and verified errors. In contrast to other work in this area, our approach requires minimal smoothness assumptions on the underlying function.
Document type :
Journal articles
Complete list of metadatas

Cited literature [5 references]  Display  Hide  Download

Contributor : Pawel Dlotko <>
Submitted on : Thursday, October 11, 2018 - 11:17:52 AM
Last modification on : Thursday, October 11, 2018 - 11:29:20 AM
Long-term archiving on : Saturday, January 12, 2019 - 1:38:48 PM


Files produced by the author(s)


  • HAL Id : hal-01706695, version 1


Pawel Dlotko, Thomas Wanner. Rigorous cubical approximation and persistent homology of continuous functions. Computers and Mathematics with Applications, Elsevier, 2018. ⟨hal-01706695⟩



Record views


Files downloads