In this video we give the functional analysis definition of a Reproducing Kernel Hilbert space, and then we investigate approximations within this space using moments as data. We draw a comparison with polynomial best approximations over L^2, and get comparable results with a new basis function made from kernels.
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Holger Wendland - Scattered Data Approximation https://amzn.to/4daHtem
Gregory Fasshauer - Meshfree Approximation Methods with MATLAB https://amzn.to/3U1KMeM
Gregory Fasshauer - Kernel Based Approximation Methods using MATLAB https://amzn.to/4d1CwEx
Ingo Steinwart and Andreas Christmann - Support Vector Machines https://amzn.to/4d5C7km
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This content is partially supported by National Science Foundation - Award ID 2027976, Air Force Office Of Scientific Research - Award FA9550-20-1-0127 and FA9550-21-1-0134. I am responsible for all opinions and content, and what I say does not necessarily reflect the sponsoring organizations.
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0:00 Start
1:11 Reproducing Kernel Hilbert Spaces
5:01 Two Examples
12:01 Customizing Bases for Approximation
14:22 Comparing Best Approximations
21:03 Wrap up and Watch Next