An experimental approach to the S-SNIEP using algebraic geometry
Date:
Abstract: The stochastic symmetric nonnegative inverse eigenvalue problem (S-SNIEP) asks for the necessary and sufficient conditions for a list of real numbers to be the spectra of a stochastic symmetric nonnegative matrix. Using tools from algebraic geometry, it is shown that the S-SNIEP is solvable by polynomial inequalities and the reality condition. An experimental approach is then presented for forming the desired feasibility region of the S-SNIEP for small matrices. This approach is then used to generate a conjectured solution to the n=4 case. We conclude by giving short comings to this approach and potential future ideas.