Timeline for Optimal $L^2$ bounds of cubic spline interpolation
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2021 at 15:09 | history | edited | gmvh | CC BY-SA 4.0 |
Added DOI link for cited paper, added tag
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| Oct 28, 2018 at 20:59 | vote | accept | Amir Sagiv | ||
| Aug 15, 2018 at 12:34 | answer | added | Iddo Hanniel | timeline score: 3 | |
| Aug 8, 2018 at 5:27 | comment | added | Amir Sagiv | @IddoHanniel yes, it is still possible that there's a better $L^2$ bound, either a better rate or at least a better constant $C$. If there isn't, where's the counter-example? | |
| Aug 7, 2018 at 16:02 | comment | added | Iddo Hanniel | If I understand correctly you want a bound on $\|f(x)-s(x)\|_2 = \sqrt{\int_a^b (f(x)-s(x))^2 dx}$. Since you have a bound $\left | f(x)-s(x) \right | \leq C h^4 = M$ (from Hall & Meyer), then $\sqrt{\int_a^b (f(x)-s(x))^2 dx} \leq \sqrt{M^2(b-a)} = C h^4 \sqrt{(b-a)} $. Doesn't that give you a sufficient $L_2$ bound? or am I missing something? | |
| Feb 27, 2018 at 5:09 | history | edited | Amir Sagiv | CC BY-SA 3.0 |
writing more concise
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| Feb 26, 2018 at 21:51 | history | asked | Amir Sagiv | CC BY-SA 3.0 |