Timeline for Can anything be said about the roots of the L4 center?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 9, 2022 at 16:30 | vote | accept | user19087 | ||
| Jan 9, 2022 at 15:01 | comment | added | Jukka Kohonen | Yes, it is a quite natural thought that this could happen, but as you can see from the strict convexity (or, from the fract that the derivative is strictly increasing as in Squala's answer), this cannot happen. There will be only one real minimum (of the sum of fourth powers) / only one real root (of the derivative). With small exponents things will be different. | |
| Jan 7, 2022 at 2:26 | comment | added | user19087 | @Jukka Kohonen I was thinking that if $x$ was a list with two clusters, then the midpoint of each cluster could each be a minimum and the midpoint between both clusters a maximum. It's too easy to imagine a sum of convex functions as $min(f_1,f_2)$ by forgetting there are no vertical asymptotes. Not something I was ever taught but easy to google or verify by plotting. | |
| Jan 6, 2022 at 20:12 | review | Close votes | |||
| Jan 21, 2022 at 3:03 | |||||
| Jan 6, 2022 at 17:26 | answer | added | Squala | timeline score: 2 | |
| Jan 6, 2022 at 13:34 | comment | added | Jukka Kohonen | Each term $(x_i-s)^4$ is a strictly convex function in $s$, so the sum $\sum_i$ is also strictly convex, so only one minimum...? | |
| S Jan 6, 2022 at 4:04 | review | First questions | |||
| Jan 6, 2022 at 4:15 | |||||
| S Jan 6, 2022 at 4:04 | history | asked | user19087 | CC BY-SA 4.0 |