I wrote the question: What can I do with this algorithm? Before writing the question I was unsure what stackexchange forum I should have posted in. I narrowed it down to either Computer Science, Computational Science, Mathematics, MathOverFlow, or Physics. I chose Computer Science, because I wanted to know if the algorithm was known. The algorithm's unknown application might be too far removed from the realm of Computer Science. May someone else suggest a better forum?

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    $\begingroup$ I don't think yours is a good question anywhere on SE. You define a problem for which you apparently have no reference, and give an algorithm. Now you expect people to tell you if your work matters. Researching the literature to find at least mention of this or a a similar problem is your task. $\endgroup$ – Raphael Jan 5 '16 at 15:25
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    $\begingroup$ I tend to agree with @Raphael. It actually seems to me your approach is a bit strange: why did you even write this algorithm in the first place? I'd assume you had at least some kind of an idea what you could do with it. At the very least, would you expect the application be in signal processing? Image processing? Something else? This information might help in googling. $\endgroup$ – Juho Jan 5 '16 at 16:10
  • $\begingroup$ @Juho Good question. I wrote it because it might have an application in solving for eigenvalues. All irreducible matrices in the OP have plus or minus one for eigenvalues. However I recently discovered there already exists algorithms that solve for eigenvalues in $\mathcal{O}(N^2)$ steps. $\endgroup$ – linuxfreebird Jan 5 '16 at 16:38

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