Timeline for Shape, shift and scaling retrieval of a sampled function
Current License: CC BY-SA 4.0
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| Feb 22, 2023 at 12:31 | comment | added | Iosif Pinelis |
@dff : You may want to try to minimize a characteristic of the discrepancy other than the quadratic characteristic $Q$ in my answer. However, I don't have a hope for that. As described in the answer, the problems are that the space to search over is high-dimensional and condition (3) may be satisfied, locally, just approximately, which can result in a large number of quasi-global minima, with values very close to $0$. BTW, somewhat unusually, the Mathematica command NMinimize that I used takes a long time in the cases I have tried, apparently trying a very large number of local minima.
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| Feb 22, 2023 at 8:15 | comment | added | dff | Thanks for the detailed answer. Interesting that Mathematica already has problems with the $n=5$ case. Can I conclude from your answer that you don't see a more algorithmic approach to solving this problem, besides looking for minimizers in a 3n dimensional space using numerical solvers? | |
| Feb 21, 2023 at 2:35 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Feb 21, 2023 at 2:24 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Feb 19, 2023 at 22:06 | comment | added | dff | Good observations. I tried to add some more conditions to my question to guarantee uniqueness of the solution... Practically, I am only interested in finding $g(x)=a f(x)+b$ for some arbitrary $a$ and $b$. | |
| Feb 19, 2023 at 21:12 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Feb 19, 2023 at 19:48 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Feb 19, 2023 at 19:34 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |