Rigorous cubical approximation and persistent homology of continuous functions

DOI10.1016/j.camwa.2017.11.027zbMath1409.41014arXiv1610.03833OpenAlexW2577615791MaRDI QIDQ1732427

Thomas Wanner, Paweł Dłotko

Publication date: 25 March 2019

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.03833

zbMATH Keywords

rigorous computationspersistent homologyconstructive version of simplex approximation theoremrigorous approximation of functionsrigorous arithmetic

Mathematics Subject Classification ID

Multidimensional problems (41A63) Other homology theories in algebraic topology (55N35)

Uses Software

• Gudhi
• Perseus
• PHAT
• Dionysus
• Persistence Landscape

Cites Work

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• Hausdorff stability of persistence spaces
• Morse theory for filtrations and efficient computation of persistent homology
• Coreduction homology algorithm for inclusions and persistent homology
• Coreduction homology algorithm for regular CW-complexes
• A persistence landscapes toolbox for topological statistics
• Stability of persistence diagrams
• Derived eigenvalues of symmetric matrices, with applications to distance geometry
• The theory of multidimensional persistence
• An optimal convex hull algorithm in any fixed dimension
• Topological persistence and simplification
• Editorial: Topology in dynamics, differential equations, and data
• Topological microstructure analysis using persistence landscapes
• Mathematical challenges in a new phase of materials science. Proceedings of the RIMS international conference, Kyoto, Japan, August 4--8, 2014
• Affine arithmetic: concepts and applications
• Betti numbers in multidimensional persistent homology are stable functions
• A Randomized Subdivision Algorithm for Determining the Topology of Nodal Sets
• PHAT – Persistent Homology Algorithms Toolbox
• On $\varepsilon $ approximations of persistence diagrams
• The Structure and Stability of Persistence Modules
• Persistent Homology under Non-uniform Error
• Introduction to Interval Analysis
• Verified Homology Computations for Nodal Domains
• Proximity of persistence modules and their diagrams

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