Smooth Interpolation Function in One Dimension | Smooth Interpolation Function E1
Автор: EpsilonDelta
Загружено: 2022-08-16
Просмотров: 345900
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This video gives a detailed construction of transition function for various levels of smoothness.
Sketch of proofs for 4 theorems regarding smoothness:
https://kaba.hilvi.org/homepage/blog/...
Faà di Bruno's formula:
https://en.wikipedia.org/wiki/Fa%C3%A...
Proof that e^(-1/x) is smooth:
https://en.wikipedia.org/wiki/Non-ana...
Chapters:
00:00 Intro
00:10 Definition of Smoothness
01:29 Hermite Interpolating Polynomials
04:32 Step Function
05:56 Auxiliary Theorems
08:43 Constructing Smooth Step Function
13:30 Main Problem
13:51 Outro
🎵Music provided by BGM President
🎵Track : Some Vintage Mood 7 - • [Royalty Free Music] Some Vintage Mood 7 (...
Corrections:
08:04 for the first theorem, f should be f'
08:15 for (2), it should be f(x) ≠ 0
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