Smooth Interpolation Function in One Dimension | Smooth Interpolation Function E1
#SoME2 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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