Evaluating the boundary and Stieltjes transform of limiting spectral distributions for random matrices with a separable variance profile
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We present numerical algorithms for solving two problems encountered in random matrix theory and its applications. First, we compute the boundary of the limiting spectral distribution for random matrices with a separable variance profile. Second, we evaluate the Stieltjes transform of such a distribution at real values exceeding the boundary. Both problems are solved with the use of Newton's method. We prove the correctness of the algorithms from a detailed analysis of the master equations that characterize the Stieltjes transform. We demonstrate the algorithms' performance in several experiments.
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