We present an algorithm for computing a factorization A = GG* for an n X n Hermitian positive definite matrix A, where both A and G have the same recursively low-rank compressed structure. This factorization is a Cholesky factorization in a general sense, because the factor G is not (block) triangular. Both time and storage costs are O(n). The factorization can be used for sampling a multivariate normal distribution or a Gaussian process, where A is the (compressed) covariance matrix. In this case, a Gaussian sample is the mean vector plus the matrix-vector product of G with a random vector from the standard Gaussian. The matrix-vector product can be formed by using an O(n) algorithm discussed in [6].
By: Jie Chen
Published in: RC25499 in 2014
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