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Beatson, R.K.* ; zu Castell, W. ; Schrödl, S.J.

Kernel-based methods for vector-valued data with correlated components.

SIAM J. Sci. Comput. 33, 1975-1995 (2011)
Open Access Green as soon as Postprint is submitted to ZB.
This paper concerns kernel-based interpolation methods for vector data with correlated components. It gives conditions for a matrix kernel to be conditionally positive definite in an appropriate sense. The conditions allow construction of matrix kernels from nonsymmetric mixtures and scalings of scalar kernels. In particular the kernel used to model the influence of component i on component j can be different from that used to model the influence of component j on component i. The vector modeling techniques considered are particularly appropriate when there are relatively few measurements of one quantity and relatively many of another "correlated" quantity. The paper concludes with some numerical tests on model problems.
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Publication type Article: Journal article
Document type Scientific Article
Keywords kernel-based methods; matrix conditionally positive definite; correlated components; interpolation; radial basis functions; machine learning; geostatistics
ISSN (print) / ISBN 1064-8275
e-ISSN 1095-7197
Quellenangaben Volume: 33, Issue: 4, Pages: 1975-1995 Article Number: , Supplement: ,
Publisher Society for Industrial and Applied Mathematics (SIAM)
Reviewing status Peer reviewed