Timeline for Linear approximation of multivariate function of bounded second order partial derivatives
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 3, 2023 at 11:05 | comment | added | Jjj | Thanks! Well, then I guess (if i have done it correctly) that the maximum value is the dimension d? Doest it seem correct? | |
| Jun 3, 2023 at 10:58 | comment | added | Jochen Wengenroth | $\sum_{j.k} x_j x_k =\left(\sum_k x_k\right)^2$ should help. | |
| Jun 3, 2023 at 10:23 | comment | added | Jjj | I tried it now but cant manage to solve it using lagrange multipliers | |
| Jun 2, 2023 at 15:07 | comment | added | Jochen Wengenroth | Did you try to maximize $\sum x_jx_k$ subject to $\sum x_j^2=1$? | |
| Jun 2, 2023 at 11:29 | comment | added | Jjj | @JochenWengenroth Thanks, but maybe it is possible to get a linear dependence on $d$ instead of a quadratic one that I obtained above? | |
| Jun 2, 2023 at 11:23 | comment | added | Jochen Wengenroth | For $r=1$ and $x=d^{-1/2}(1,1,\ldots,1)$ you have $\sum_{j,k=1}^d |x_jx_k|= d$. There does not seem to be reasonnable bound independent of the dimension. | |
| S Jun 2, 2023 at 10:32 | review | First questions | |||
| Jun 2, 2023 at 10:58 | |||||
| S Jun 2, 2023 at 10:32 | history | asked | Jjj | CC BY-SA 4.0 |