2019/09/16 by Yiting Zhang, Zhang, Yiting, Thomas Trogdon +1
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1909.07506
openalex publication_date 2019/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a random matrix A with eigenvalues between -1 and 1, we analyze the number of iterations needed to solve the linear equation (I-A)x=b with the Neumann series iteration. We give sufficient conditions for convergence of an upper bound of the iteration count in distribution. Specifically, our results show that when the scaled extreme eigenvalues of A converge in distribution, this scaled upper bound on the number of iterations will converge to the reciprocal of the limiting distribution of the largest eigenvalue.