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Given a random matrix A with eigenvalues between -1 and 1, we analyze thenumber of iterations needed to solve the linear equation (I-A)x=b with theNeumann series iteration. We give sufficient conditions for convergence of anupper bound of the iteration count in distribution. Specifically, our resultsshow that when the scaled extreme eigenvalues of A converge in distribution,this scaled upper bound on the number of iterations will converge to thereciprocal of the limiting distribution of the largest eigenvalue.

A Probabilistic Analysis of the Neumann Series Iteration