Timeline for Error of midpoint method for differentiable functions
Current License: CC BY-SA 3.0
3 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Feb 19, 2014 at 17:05 | comment | added | James Propp | Sketch of a possible proof: Write $f(x)$ as the sum of a quadratic function $g(x)$ and a function $h(x)$ satisfying $h(0)=h(1)$ and $h'(0)=h'(1)$. Prove the $o(1/n)$ estimate for $g(x)$ by direct computation and for $h(x)$ by Fourier methods (treating $h$ as a differentiable function on ${\bf R}/{\bf Z}$) and then add to get the $o(1/n)$ estimate for $f$. But is the needed lemma about differentiable functions on the circle true? | |
| Feb 18, 2014 at 22:45 | history | asked | James Propp | CC BY-SA 3.0 |