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Background: Having failed to solve a general problem that I posted more than a year ago on mathoverflow.net, I have now resorted to numerical methods (involving finite probability distributions) . This has resulted in probabilities of events given by sums of polynomial degree n terms each obtained from a probability generating function . The terms are functions of n decision variables subject to linear constraints. Off the shelf, numerical non-linear optimisation methods are at present being used to optimise the decision variables. Even for small problems, n=4 , there are some minor choice of algorithm questions and I would like to solve up to n=16: there are English county chess teams of 16 players. I trust Normality will kick in before n=16

Question: What is the convention here about seeking literature references and relative expert opinion about numerical methods for special structure problems , related to (probability) problems which have so far escaped analytical treatment? More colloquially, what can a poster get away with?

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We have the tag for numerical analysis and for reference requests, and making a reference request for numerical results can be on-topic. If you ask a well motivated reference request for mathematical aspects of numerical methods to certain problem types, I see no problem. If you are interested in practical coding issues or other less mathematical aspects of the problem, then there probably is a more suitable SE site for it. Many problems admit "analytical treatment", but that does not always mean closed form solutions, so there can be significant mathematical literature on problems that cannot be solved explicitly enough with analytical tools.

I think the best way to find good conventions for such questions is to look at examples. I suggest searching MathOverflow with [reference-request] [na.numerical-analysis] (link). Throw in more tags and keywords if you wish. Find questions that have positive score and have received useful answers to see what works well here.

Asking for expert opinions rather is trickier than asking for references, since such questions are in danger of being closed as primarily opinion-based. It might be better not to ask for opinions explicitly — a reference request already does so implicitly, to some extent at least.

I am not an expert in your field, but it seems to me that your question could be made into a reasonable MO question.

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    $\begingroup$ +1 for "more suitable SE site". Some questions on numerical methods should be in MO, others not. $\endgroup$ – Gerald Edgar Jul 19 '15 at 12:38

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