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

Alexander Litvinenko

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arXiv · 1709.08625

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

Alexander Litvinenko

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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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BibTeX RIS

Alexander Litvinenko. 2017-09-24. HLIBCov: Parallel Hierarchical Matrix Approximation of Large Covariance Matrices and Likelihoods with Applications in Parameter Identification. https://arxiv.org/abs/1709.08625

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