What is it about?

We applied hierarchical (H-) matrices [Hackbusch 99] for approximating covariance matrices and computing Karhunen-Loeve expansion. The H-matrix techniques allows us to do it with O(n log n) computational complexity and storage cost.

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Why is it important?

Such low computational cost allows us to consider much larger matrices and much larger (better resolved) random fields and random processes. This could be useful, for instance, for multi-scale problems. Additionally, H-matrices allow us to consider more generous covariance matrices (and not only those which depend on the distance |x-y|).


With this article we started to introduce the H-matrix technique, which was initially developed for numerical solution of PDEs and integral equations, to statisticians for solving statistical and stochastic problems.

Dr. Alexander Litvinenko
Rheinisch Westfalische Technische Hochschule Aachen

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This page is a summary of: Application of hierarchical matrices for computing the Karhunen–Loève expansion, Computing, October 2008, Springer Science + Business Media, DOI: 10.1007/s00607-008-0018-3.
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