Math Forum :: View topic – System of linear inequalities

Recently I have been writing a program. It is basically done, but I want to improve its efficiency. I face the following problem. Given an n by 3 real matrix A, I need to find one (but not all) solution x in R^3 of the system of inequalities Ax > 0. (You may assume the system is solvable.) I hope the complexity is at most O(n^2). I tried Fourier-Motzkin method, but then I faced another problem of detecting redundant inequalities; the number of inequalities increases dramatically during the process of Fourier-Motzkin elimination. Any help is appreciated._________________