Timeline for Can this nonlinear vector equation be solved analytically?
Current License: CC BY-SA 3.0
10 events
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| Mar 20, 2017 at 21:22 | comment | added | Daniel Turizo | As I said earlier, I do not much about linear algebra. When I reached this equation for the first time I thought it would be possible to solve it, but I failed and ended up asking the question here. As I started to read more about the topic I realised that's probably not the case. | |
| Mar 20, 2017 at 21:12 | comment | added | Suvrit | The way edit2 is posed, isn't that almost as general as any system of quadratic equations? So I am not sure why you'd expect a "closed form"? | |
| Mar 20, 2017 at 4:15 | comment | added | Daniel Turizo | @Suvrit you are right. The equation of "edit2" is obtained by doing a linear combination of the scalar equations of the original vector equation. I suspect the equations are equivalent as long as A is non-singular. As for the numerical solvers, I will consider it. It seems like an analytic solution is a no-go, but I do not want to lose hope. | |
| Mar 20, 2017 at 3:57 | comment | added | Suvrit | You could look into solving a system of quadratic equations (for edit2); there are a few solvers (e.g., Bertini) for numerically solving systems of polynomial equations. (I am not sure that all your formulations are equivalent though! e.g., in edit2, if $A=0$, then $x=0$ provides a solution, whereas this is not the case for the other versions). | |
| Mar 20, 2017 at 2:27 | comment | added | Daniel Turizo | I am not supposing an analytical solution exists, that is in fact my question. For me an answer like "the equation can be solved using X" is as valid as "no closed solution exists because of Y" or "your question cannot be answered because what is known about that type of equation is Z". I am sorry if I am asking for something akin to magic, but I am not that knowledgeable about linear algebra. | |
| Mar 20, 2017 at 0:49 | comment | added | Michael Renardy | I am tempted to vote to close, but I cannot find a reason. Unfortunately "asking for something akin to magic" is not offered as a choice. | |
| Mar 19, 2017 at 15:25 | history | edited | Daniel Turizo | CC BY-SA 3.0 |
New equivalent equation.
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| Mar 15, 2017 at 22:48 | history | edited | Daniel Turizo | CC BY-SA 3.0 |
added 328 characters in body
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| Mar 15, 2017 at 22:17 | review | First posts | |||
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| Mar 15, 2017 at 22:16 | history | asked | Daniel Turizo | CC BY-SA 3.0 |