Advances in Computational Mathematics

, Volume 29, Issue 3, pp 269–290 | Cite as

Improved stability estimates and a characterization of the native space for matrix-valued RBFs



In this paper we derive several new results involving matrix-valued radial basis functions (RBFs). We begin by introducing a class of matrix-valued RBFs which can be used to construct interpolants that are curl-free. Next, we offer a characterization of the native space for divergence-free and curl-free kernels based on the Fourier transform. Finally, we investigate the stability of the interpolation matrix for both the divergence-free and curl-free cases, and when the kernel has finite smoothness we obtain sharp estimates.


Divergence-free Radial basis functions Stability Native spaces Interpolation 

Mathematics Subject Classifications (2000)

41A05 41A30 41A63 65Dxx 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUnited States Military AcademyWest PointUSA

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