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Licensed Unlicensed Requires Authentication Published by De Gruyter May 20, 2015

Numerical Methods of Karhunen–Loève Expansion for Spatial Data

  • Juan Hu EMAIL logo and Hao Zhang
From the journal Economic Quality Control


With the development of technology, a large amount of spatial data are usually observed in many applications. These massive spatial data impose a challenge to the traditional spatial data analysis primarily because of the large covariance matrix. One way to overcome the computation burden is to utilize a low rank model. The optimal low rank model is provided by the Karhunen–Loève (KL) expansion of the spatial process. However, the inference and prediction of the spatial data require an efficient algorithm for the KL expansion. In this paper, we compare four algorithms that have been proposed to numerically obtain the KL expansion. It is found that the Gaussian quadrature method outperforms the others for spatial processes.

MSC: 60-07

Funding source: National Science Foundation

Award Identifier / Grant number: US grant IIS-1028291

Received: 2014-10-21
Revised: 2014-12-10
Accepted: 2014-12-14
Published Online: 2015-5-20
Published in Print: 2015-6-1

© 2015 by De Gruyter

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