Timeline for Upper bound for an inverse Laplace transform
Current License: CC BY-SA 4.0
15 events
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| May 15, 2023 at 9:25 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| May 11, 2023 at 23:37 | comment | added | Yaroslav Bulatov | @DieterKadelka I got it by calling Mathematica Asymptotic to get expansion around s=0 . However it's was not clear to me how it decided to use the Puiseux series with the correct leading fractional exponent for this expression | |
| May 11, 2023 at 20:01 | answer | added | Christophe Leuridan | timeline score: 3 | |
| May 11, 2023 at 16:52 | comment | added | Dieter Kadelka | By the way, $s \to g_{gsd}(s) * \sqrt s$ seems to be concave and increasing from $0$ to $\sqrt{\frac{3\pi}{50}}$. If this function is concave indeed then it must be increasing. Concavity may be simpler to show. | |
| May 11, 2023 at 16:25 | comment | added | Dieter Kadelka | Seems to be correct. I got $g_{gsd}(1e10)*1e5 = 0.434160752718722$. And for $s=1e20$ the difference is $-1.665..10^{-16}$. How did you identify this constant? Very interestingly. | |
| May 11, 2023 at 13:20 | comment | added | Yaroslav Bulatov | @DieterKadelka btw, the 0.433 constant appears to be $\sqrt{\frac{3\pi}{50}}$ | |
| May 11, 2023 at 10:24 | history | edited | Yaroslav Bulatov | CC BY-SA 4.0 |
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| May 11, 2023 at 8:48 | history | edited | Yaroslav Bulatov | CC BY-SA 4.0 |
added Dieter's Kadelka's simulation
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| May 11, 2023 at 6:17 | comment | added | Yaroslav Bulatov | Yes, for theoretical purposes. Proving bounds on the limit in your comment would be a very nice result. This would show that SGD stays within a small constant factor of GD for this problem, ie, that it has the same "convergence rate" | |
| May 10, 2023 at 22:45 | comment | added | Dieter Kadelka | Why do you not calculate $g_{sgd}$ with numerical methods directly, as mentioned in the above link "a particular"? Wolfram Notebook should do it. The resulting function looks similar as that of $g_{gd}$ and in particular $g_{sgd}(0.1)=0.3272708709647729$ and $g_{sgd}(20)=0.095291845071114367$ Is the upper bound for theoretical purposes? (Calculations done with my program). | |
| May 10, 2023 at 22:36 | comment | added | Dieter Kadelka | Looks like $s \to g_{sgd}(s)∗\sqrt s$ is increasing and $\lim_{s \to \infty} g_{sgd}(s)∗\sqrt s$ about 0.433. | |
| May 10, 2023 at 20:48 | history | edited | LSpice | CC BY-SA 4.0 |
Removing editorialising in title
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| May 10, 2023 at 19:16 | history | edited | Yaroslav Bulatov | CC BY-SA 4.0 |
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| May 10, 2023 at 19:02 | history | edited | Yaroslav Bulatov | CC BY-SA 4.0 |
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| May 10, 2023 at 18:56 | history | asked | Yaroslav Bulatov | CC BY-SA 4.0 |