Timeline for One-sided version of the "best approximation polynomial" : Upper polynomial approximations
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 31, 2011 at 11:20 | comment | added | Sergei Ivanov | For every fixed $x\in X$, the requirement that $h(x)\ge f(x)$ is a linear inequality on the coefficients of $f$. So $S$ is a convex polyhedral set and therefore has finitely many extremal points. And $M(S)$ is the boundary of $S$. | |
| Oct 31, 2011 at 11:08 | comment | added | Ewan Delanoy | @Douglas : you're absolutely right. Note that your family of examples is actually the convex hull between $h_{-1}$ and $h_1$, so perhaps looking at extremal elements inside those maximal elements yields a really finite set this time. | |
| Oct 31, 2011 at 11:06 | history | edited | Ewan Delanoy | CC BY-SA 3.0 |
added update
|
| Oct 31, 2011 at 9:59 | comment | added | Douglas Zare | If $d=1$ and $X=\{-1,0,1\}$ and $f(x) = -x^2$ on these points, then aren't all $h_c$ minimal where $h_c(x) = cx, -1 \le c \le 1$? | |
| Oct 31, 2011 at 9:20 | history | asked | Ewan Delanoy | CC BY-SA 3.0 |