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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)
Verlagsversion DOI
Open Access Green möglich sobald Postprint bei der ZB eingereicht worden ist.
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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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter 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 Band: 33, Heft: 4, Seiten: 1975-1995 Artikelnummer: , Supplement: ,
Verlag Society for Industrial and Applied Mathematics (SIAM)
Begutachtungsstatus Peer reviewed