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Foundations of Computational Mathematics

, Volume 19, Issue 5, pp 991–1011 | Cite as

Interpolation, the Rudimentary Geometry of Spaces of Lipschitz Functions, and Geometric Complexity

  • Shmuel WeinbergerEmail author
Article
  • 129 Downloads

Abstract

We consider seriously the analogy between interpolation of nonlinear functions and manifold learning from samples, and examine the results of transferring ideas from each of these domains to the other. Illustrative examples are given in approximation theory, variational calculus (closed geodesics), and quantitative cobordism theory.

Keywords

Interpolation Function space Persistent homology Homotopy Quantitative cobordism Embedding 

Mathematics Subject Classification

Primary 68U05 57R75 41A10 Secondary 55Q05 68T10 

Notes

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Copyright information

© SFoCM 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

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