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.
Photo by Tim Johnson on Unsplash
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|).
Read the Original
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.
You can read the full text:
The following have contributed to this page