Timeline for Forcing the fit of a nonlinear piecewise function to be continuous
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 30, 2020 at 21:33 | vote | accept | Ely Eastman | ||
| Mar 30, 2020 at 20:44 | answer | added | Bob Hanlon | timeline score: 4 | |
| Mar 30, 2020 at 20:13 | comment | added | JimB |
If you want the function to be continuous (but not necessarily having the derivative to be continuous) at $t=600$, then you need to have $A \exp \left(-\left(\frac{t-\text{t0}}{\sqrt{2} \sigma }\right)^2\right)=B \exp \left(-\frac{t-\text{t1}}{\tau }\right)$ when $t=600$. That means there will be some restrictions among the parameters. Using Reduce on that equality suggests that using $\tau=-\frac{2 \sigma ^2 (t_1-600)}{2 \sigma ^2 \log \left(\frac{B}{A}\right)+t_0^2-1200 t_0+360000}$ would do it.
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| Mar 30, 2020 at 19:48 | comment | added | Ely Eastman | I need the function to be continuous because I am trying to deconvolve it with another function and want to minimize as much noise as possible in the deconvolution. | |
| Mar 30, 2020 at 19:44 | history | asked | Ely Eastman | CC BY-SA 4.0 |