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Reconstructing functions from random samples

Abstract:

From a sufficiently large point sample lying on a compact Riemannian submanifold of Euclidean space, one can construct a simplicial complex which is homotopy-equivalent to that manifold with high confidence. We describe a corresponding result for a Lipschitz-continuous function between two such manifolds. That is, we outline the construction of a simplicial map which recovers the induced maps on homotopy and homology groups with high confidence using only finite sampled data from the domain a...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.3934/jcd.2014.1.233

Authors


Mischaikow, K More by this author
Publisher:
American Institute of Mathematical Sciences Publisher's website
Journal:
Journal of Computational Dynamics Journal website
Volume:
1
Issue:
2
Pages:
233-248
Publication date:
2014-12-01
DOI:
ISSN:
2158-2491
Pubs id:
pubs:673279
URN:
uri:b3f08ed6-42bf-48cb-bdc1-4453176db347
UUID:
uuid:b3f08ed6-42bf-48cb-bdc1-4453176db347
Local pid:
pubs:673279
Keywords:

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