Compactly supported radial covariance functions |
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Authors: | G Moreaux |
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Institution: | (1) La Roque de Scieurac, 32100 Condom, France |
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Abstract: | The Least-squares collocation (LSC) method is commonly used in geodesy, but generally associated with globally supported covariance
functions, i.e. with dense covariance matrices. We consider locally supported radial covariance functions, which yield sparse
covariance matrices. Having many zero entries in the covariance matrice can both greatly reduce computer storage requirements
and the number of floating point operations needed in computation. This paper reviews some of the most well-known compactly
supported radial covariance functions (CSRCFs) that can be easily substituted to the usually used covariance functions. Numerical
experiments reveals that these finite covariance functions can give good approximations of the Gaussian, second- and third-order
Markov models. Then, interpolation of KMS02 free-air gravity anomalies in Azores Islands shows that dense covariance matrices
associated with Gaussian model can be replaced by sparse matrices from CSRCFs resulting in memory savings of one-fortieth
and with 90% of the solution error less than 0.5 mGal.
This article is dedicated to Cerbère. |
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Keywords: | Least-squares Comactly supported covariance functions Large linear systems Sparse matrices |
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