The problem of minimizing and of maximizing the spectral radius on a set of matrices is notoriously hard. Nevertheless, for some sets of a special structure that problem admits an efficient solution. We consider sets of nonnegative matrices with independent row uncertainties. Remarkable properties of such sets were discovered by V.Blondel and Y.Nesterov in 2009, although their applications in the game theory, in the theory of asynchronous systems, etc. were studied before. The ``spectral simplex method’’ for maximizing/minimizing the spectral radius over such sets demonstrates its surprising efficiency. We prove its convergence, estimate the rate, and discuss applications to dynamical systems, mathematical economics, etc. A link to a well-known problem of indicators in the population dynamics will also be shown.