Wikipedia:Reference desk/Archives/Mathematics/2015 October 31

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October 31

Constrained simultaneous equation solutions

Given a set of linear simultaneous equations with multiple solutions -- say five equations in eight variables for the sake of argument -- how do I go about determining whether there is any solution with all variables within a certain range (e.g. all >= 0 and <= 1)? Is there a systematic method for doing this? 86.152.161.137 (talk) 02:52, 31 October 2015 (UTC)

... PS, I don't want a "trial and error" method, like solve for dependent variables and free variables, and the try a whole bunch of test values for the free variables. I already know how to do that method, but it kind of sucks ... 86.152.161.137 (talk) 03:31, 31 October 2015 (UTC)

This falls under linear programming or perhaps convex polytopes. The way you've stated it, it sounds like it should be a variation solving linear equations, but once you throw inequalities into the mix things get much more complicated. --RDBury (talk) 09:54, 31 October 2015 (UTC)

Yes, this is the problem of determining feasibility of a linear programming problem. A standard simplex implementation will do this as phase I of the algorithm: typically use an objective that measures the sum of violations of the inequalities and solve the resulting problem by the simplex method. 165.120.165.97 (talk) 23:18, 31 October 2015 (UTC)

Thanks for the replies. It is probably too complicated for me to understand. 86.152.161.137 (talk) 03:17, 1 November 2015 (UTC)

For understanding first try zero equations in one variable. 0≤x≤1. Bo Jacoby (talk) 07:56, 1 November 2015 (UTC).