Timeline for Bounds on coefficients $c_i$ of Chebyshev expansion $f(x) = \sum_{k=0}^{n} c_kT_k(x) : [-1,1] \mapsto [-1,1]$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 26, 2021 at 7:36 | comment | added | NickVO | Yes, I think this is the kind of bound I need. Thank you! Do you happen to have a source that I could refer to? | |
| Apr 16, 2021 at 18:41 | comment | added | Will Sawin | One has $\int_{0}^{2 \pi } T_k( \cos \theta) \cos ( \ell \theta ) d\theta $ is $\pi$ if $\ell$ is $\pm k$ and $0$ otherwise. So $\int_{0}^{2\pi} f(\cos \theta) \cos(\ell \theta) d\theta=\pi c_\ell$ and thus $|c_\ell| \leq \frac{1}{ \pi} \int_{0}^{ 2\pi} | \cos(\ell \theta) | d \theta = \frac{4}{\pi}$. So $c_\ell$ can never be more than $\frac{4}{\pi}$ for any $\ell$. Is this the kind of bound you are looking for? | |
| Apr 16, 2021 at 17:53 | review | First posts | |||
| Apr 16, 2021 at 18:41 | |||||
| Apr 16, 2021 at 15:11 | history | edited | NickVO | CC BY-SA 4.0 |
added 148 characters in body
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| Apr 16, 2021 at 15:03 | history | asked | NickVO | CC BY-SA 4.0 |