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Journal of Computational Dynamics (JCD)
 

Reconstructing functions from random samples
Pages: 233 - 248, Issue 2, December 2014

doi:10.3934/jcd.2014.1.233      Abstract        References        Full text (432.0K)           Related Articles

Steve Ferry - Department of Mathematics, Rutgers University, Piscataway, NJ 08854, United States (email)
Konstantin Mischaikow - Rutgers University, 110 Frelinghusen Road, Piscataway, NJ 08854, United States (email)
Vidit Nanda - Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104, United States (email)

1 A. Bjorner, Nerves, fibers and homotopy groups, Journal of Combinatorial Theory, Series A, 102 (2003), 88-93.       
2 K. Borsuk, On the imbedding of systems of compacta in simplicial complexes, Fundamenta Mathematicae, 35 (1948), 217-234.       
3 G. Carlsson, Topology and data, Bulletin of the American Mathematical Society, 46 (2009), 255-308.       
4 J.-G. Dumas, F. Heckenbach, B. D. Saunders and V. Welker, Computing simplicial homology based on efficient Smith normal form algorithms, Proceedings of Algebra, Geometry and Software Systems, (2003), 177-206.       
5 H. Edelsbrunner and J. L. Harer, Computational Topology - an Introduction, American Mathematical Society, Providence, RI, 2010.       
6 K. Fischer, B. Gaertner and M. Kutz, Fast-smallest-enclosing-ball computation in high dimensions, Proceedings of the $11^{th}$ Annual European Symposium on Algorithms (ESA), 2832 (2003), 630-641.
7 R. Ghrist, Three examples of applied and computational homology, Nieuw Archief voor Wiskunde, 9 (2008), 122-125.       
8 A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.       
9 S. Harker, K. Mischaikow, M. Mrozek and V. Nanda, Discrete Morse theoretic algorithms for computing homology of complexes and maps, Foundations of Computational Mathematics, 14 (2014), 151-184.       
10 T. Kaczynski, K. Mischaikow and M. Mrozek, Computational Homology, Springer-Verlag, New York, 2004.       
11 D. Kozlov, Combinatorial Algebraic Topology, Springer, 2008.       
12 J. R. Munkres, Elements of Algebraic Topology, Addison-Wesley, Menlo Park, 1984.       
13 P. Niyogi, S. Smale and S. Weinberger, Finding the homology of submanifolds with high confidence from random samples, Discrete and Computational Geometry, 39 (2008), 419-441.       
14 S. Smale, A Vietoris mapping theorem for homotopy, Proceedings of the American mathematical society, 8 (1957), 604-610.       
15 E. H. Spanier, Algebraic Topology, Springer-Verlag, New York, 1981. Corrected reprint.       

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