Discrete morse theoretic algorithms for computing homology of complexes and maps
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dc.type
JournalArticle
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dc.description.physical
151-184
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dc.abstract.en
We provide explicit and efficient reduction algorithms based on discrete Morse theory to simplify homology computation for a very general class of complexes. A set-valued map of top-dimensional cells between such complexes is a natural discrete approximation of an underlying (and possibly unknown) continuous function, especially when the evaluation of that function is subject to measurement errors. We introduce a new Morse theoretic preprocessing framework for deriving chain maps from such set-valued maps, and hence provide an effective scheme for computing the morphism induced on homology by the approximated continuous function.
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dc.description.volume
14
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dc.description.number
1
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dc.identifier.doi
10.1007/s10208-013-9145-0
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dc.identifier.eissn
1615-3383
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dc.title.journal
Foundations of Computational Mathematics
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dc.language.container
eng
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dc.affiliation
Wydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej