Uploaded April 2024 | Updated September 2026, 1 day ago
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.
//Watch Next
The Real Analysis Survival Guide youtu.be/v5rD0B-zfXw
The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XM
Introduction to Control Theory youtu.be/0v4WFmOm764
//Books
Steve Brunton and J. Nathan Kutz - Data Driven Science and Engineering amzn.to/4daHtem
Holger Wendland - Scattered Data Approximation amzn.to/4daHtem
Gregory Fasshauer - Meshfree Approximation Methods with MATLAB amzn.to/3U1KMeM
Gregory Fasshauer - Kernel Based Approximation Methods using MATLAB amzn.to/4d1CwEx
Ingo Steinwart and Andreas Christmann - Support Vector Machines amzn.to/4d5C7km
// Code
BitBucket
bitbucket.org/joelrosenfeld/rkhs-moments-approximation/src/main
Try Through MATLAB Online for free (20 hours free use per month)
matlab.mathworks.com/open/github/v1?host=bitbucket.org&repo=joelrosenfeld/rkhs-moments-approximation
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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.
DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
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
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.
//Watch Next
The Real Analysis Survival Guide youtu.be/v5rD0B-zfXw
The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XM
Introduction to Control Theory youtu.be/0v4WFmOm764
//Books
Steve Brunton and J. Nathan Kutz - Data Driven Science and Engineering amzn.to/4daHtem
Holger Wendland - Scattered Data Approximation amzn.to/4daHtem
Gregory Fasshauer - Meshfree Approximation Methods with MATLAB amzn.to/3U1KMeM
Gregory Fasshauer - Kernel Based Approximation Methods using MATLAB amzn.to/4d1CwEx
Ingo Steinwart and Andreas Christmann - Support Vector Machines amzn.to/4d5C7km
// Code
BitBucket
bitbucket.org/joelrosenfeld/rkhs-moments-approximation/src/main
Try Through MATLAB Online for free (20 hours free use per month)
matlab.mathworks.com/open/github/v1?host=bitbucket.org&repo=joelrosenfeld/rkhs-moments-approximation
//Music Provided by Epidemic Sound
Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:
epidemicsound.com/referral/644nao
//Recording Equipment
Canon SL3: amzn.to/3nZ11KU
Canon T6i: amzn.to/3FUpkQh
Rode VideoMic: amzn.to/3lhldGa
Blue Yeti Microphone: amzn.to/3I1y88N
Yeti Nano Microphone: amzn.to/3I1mriA
SanDisc 256GB SD Card: amzn.to/3E3LOOr
Neewer 5600K USB LED Lights: amzn.to/3xvB9cN
Neewer 18 inch Ring Light: amzn.to/2ZvgCsc
Camera Power Adapter: amzn.to/3D3upUu
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.
DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
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
