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Numerische Mathematik

, Volume 140, Issue 3, pp 639–676 | Cite as

Fast random field generation with H-matrices

  • Michael Feischl
  • Frances Y. Kuo
  • Ian H. Sloan
Article

Abstract

We use the H-matrix technology to compute the approximate square root of a covariance matrix in linear cost. This allows us to generate normal and log-normal random fields on general point sets with optimal cost. We derive rigorous error estimates which show convergence of the method. Our approach requires only mild assumptions on the covariance function and on the point set. Therefore, it might be also a nice alternative to the circulant embedding approach which applies only to regular grids and stationary covariance functions.

Mathematics Subject Classification

62M40 60H15 65F10 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Michael Feischl
    • 1
  • Frances Y. Kuo
    • 2
  • Ian H. Sloan
    • 2
  1. 1.Karlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.School of Mathematics and StatisticsUNSW SydneySydneyAustralia

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