In this project, I implement a parallel approximate singular value decomposition (SVD) in Julia. The approach taken here follows the algorithm described by Friedland et al., [1] and implement it using AbstractMatrices and DArrays in Julia to give the user additional flexibility. For additional speed, the algorithm makes direct calls to the DGEMV routine in the BLAS kernels. An error analysis us...

We equip the polytope of n × n Markov matrices with the normalized trace of the Lebesgue measure of Rn 2 . This probability space provides random Markov matrices, with i.i.d. rows following the Dirichlet distribution of mean (1/n, . . . , 1/n). We show that ifM is such a randommatrix, then the empirical distribution built from the singular values of √ nM tends as n → ∞ to a Wigner quarter–circl...

We prove a central limit theorem (CLT) for the product of class random singular matrices related to Hill’s equation studied by Adams–Bloch–Lagarias. The CLT features an explicit formula variance in terms distribution matrix entries and this allows exact calculation some examples. Our proof relies on novel connection theory [Formula: see text]-dependent sequences which also leads interesting pre...

This work examines various statistical distributions in connection with random Vandermonde matrices and their extension to d-dimensional phase distributions. Upper and lower bound asymptotics for the maximum singular value are found to be O(logN) and O(logN/ log logN) respectively where N is the dimension of the matrix, generalizing the results in [21]. We further study the behavior of the mini...