HLIBCov: Parallel Hierarchical Matrix Approximation of Large Covariance Matrices and Likelihoods with Applications in Parameter Identification

2017/09/24 by Litvinenko, Alexander
#62F99 #62M30 #62P12 #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #G.3 #G.4 #J.2 #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1709.08625

Abstract

We provide more technical details about the HLIBCov package, which is using parallel hierarchical (\H-) matrices to identify unknown parameters of the covariance function (variance, smoothness, and covariance length). These parameters are estimated by maximizing the joint Gaussian log-likelihood function. The HLIBCov package approximates large dense inhomogeneous covariance matrices with a log-linear computational cost and storage requirement. We explain how to compute the Cholesky factorization, determinant, inverse and quadratic form in the H-matrix format. To demonstrate the numerical performance, we identify three unknown parameters in an example with 2,000,000 locations on a PC-desktop.

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