Timeline for Function composition inside implicit function equation
Current License: CC BY-SA 4.0
15 events
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| Jul 9 at 21:21 | history | edited | albop | CC BY-SA 4.0 |
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| Jul 9 at 19:47 | comment | added | albop | ... I looked at the reference you gave , which looks for $f$ in $f(f(x))=g(x)$. I would say that my particular usecase assumes $g(0)=0$. Also, for the quadratic equation to have a solution, one needs to assume $g'(0)>0$. These assumptions are not met by any of the counterexample I see in the link. I clarified my question by adding explicitly the assumption that the quadratic equation needs to have one solution. | |
| Jul 9 at 19:37 | history | edited | albop | CC BY-SA 4.0 |
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| Jul 9 at 19:36 | history | edited | albop | CC BY-SA 4.0 |
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| Jul 9 at 19:14 | comment | added | albop | Well, what makes the problem more specific is that I'm looking for a local solution, in the neighborhood of a fixed point (0). I clarified the question to make it more obvious. I looked at the reference you gave (thanks!). | |
| Jul 9 at 19:02 | history | edited | albop | CC BY-SA 4.0 |
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| Jul 9 at 18:33 | history | edited | albop | CC BY-SA 4.0 |
Added condition f(0,0,0)=0
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| Jul 9 at 17:42 | comment | added | Christian Remling | This is hopeless in this generality. If $f(x,y,z)=g(x,z)$ and you make the usual extra assumptions that guarantee the local existence and uniqueness of a $\psi(x)$ such that $g(x,\psi(x))=0$, then you are still left with the rather intractable problem of finding a compositional square root of $\psi$. Compare here: mathoverflow.net/questions/17614/solving-ffx-gx | |
| Jul 9 at 16:55 | comment | added | albop | Thanks! I have corrected the typo and added some references. $\varphi^{(1)}$ is the first order derivative: I made that clear above. | |
| Jul 9 at 16:53 | history | edited | albop | CC BY-SA 4.0 |
Added references.
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| Jul 9 at 16:35 | history | edited | albop | CC BY-SA 4.0 |
Corrected domain of f
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| Jul 9 at 16:23 | history | edited | LSpice | CC BY-SA 4.0 |
Typo
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| Jul 9 at 16:21 | comment | added | LSpice | $f : R^n \times R^n \times \to R^n$ is surely a typo; what is it supposed to be? What are some papers where you have seen such references? What is $\varphi^{(1)}$? | |
| S Jul 9 at 16:20 | review | First questions | |||
| Jul 9 at 18:12 | |||||
| S Jul 9 at 16:20 | history | asked | albop | CC BY-SA 4.0 |