Timeline for Solving diagonal simultaneous quadratic equations
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 18, 2020 at 18:22 | comment | added | Konstantinos Kanakoglou | What are the dimensions of your $A,B,C$ matrices ? I mean, if $A,B$ are $m\times n$ and $C$ is $m\times 1$ with $m=2n$ then you can "linearize" the system and solve it as a linear system. | |
| Apr 18, 2020 at 16:14 | answer | added | DSM | timeline score: 0 | |
| Mar 22, 2019 at 17:40 | comment | added | Ben Farmer | I've tried it numerically and not found other solutions, but I haven't been very thorough about it. These are a set of extremisation conditions for finding the maximum likelihood estimator in a statistics problem, so it will be the regularity of the parameter space plus some sort of asymptotic theory guaranteeing the (asymptotic) uniqueness of the maximum likelihood estimator that means there should be only one solution, at least for sufficiently largely amounts of data. Not sure how that property will manifest in these equations though. | |
| Mar 22, 2019 at 15:15 | comment | added | Federico Poloni | Bézout's theorem tells you that generically you can expect a lot of solutions, $2^N$ of them (possibly complex). Are you sure you have only one in your case? Have you tried small-dimensional cases to check what happens there? | |
| Mar 22, 2019 at 13:24 | comment | added | Ben Farmer | Well for my cases there should usually only be one solution, I'm pretty sure. There is probably some extra structure that ensures this, but I'm afraid I'm not sure what it is. Is there some sort of equivalent of a determinant that could be computed to show this? | |
| Mar 21, 2019 at 12:52 | comment | added | Federico Poloni | Do you need one solution, or all of them? | |
| Mar 21, 2019 at 11:01 | answer | added | Rodrigo de Azevedo | timeline score: 2 | |
| Mar 18, 2019 at 19:40 | answer | added | Robert Israel | timeline score: 2 | |
| Mar 18, 2019 at 16:00 | review | First posts | |||
| Mar 18, 2019 at 16:07 | |||||
| Mar 18, 2019 at 15:56 | history | asked | Ben Farmer | CC BY-SA 4.0 |