Vector-valued Lg-splines I. Interpolating splines |
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| Authors: | Gursharan S. Sidhu Howard L. Weinert |
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| Affiliation: | Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, México 20, D.F. Mexico;Department of Electrical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218 U.S.A. |
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| Abstract: | The theory of Lg-splines developed by Jerome and Schumaker is extended to the vector-valued (multivariate) case. The extension is described in the frame-work of a reproducing-kernel Hilbert space which among other things allows the establishment of a congruent least-squares estimation problem for a vectorvalued lumped random process. The results include a dynamic recursive algorithm for vector-valued Lg-splines with EHB data and a useful structural characterization theorem for such splines. Some results on computable approximation error bounds are also included. |
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