The nonnegative inverse eigenvalue problem is solvable and the algorithm to solve it exists. So why is the problem unsolved?
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Abstract: The nonnegative inverse eigenvalue problem (NIEP) asks what are the necessary and sufficient conditions such that a list of complex numbers forms the spectra of a nonnegative matrix. In this talk, I will give some background into the NIEP and its related subproblems. Next, I will discuss how the NIEP forms a semialgebraic set and why it can then be solved by polynomial inequalities. Finally, I will give an overview of some algorithms that can give a solution to the NIEP and outline why we can’t directly use them.