05763614

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05763614 Fuselier, Edward J. Sobolev-type approximation rates for divergence-free and curl-free RBF interpolants. Math. Comput. 77, No. 263, 1407-1423 (2008). 2008 American Mathematical Society, Providence, RI EN radial basis function interpolant error estimates interpolation of multivariate function

doi:10.1090/S0025-5718-07-02096-0

The results of this paper are part of the author's dissertation. Recently, error estimates have made available for divergence-free radial basis function (RBS) interpolants. These results are only valid for functions within the associated reproducing kernel Hilbert space (RKHS) of the matrix-valued RBF. Functions within the associated RKHS, also know as the ``native space of the RBFF, can be characterized as vector fields having a specific smoothness, making the native quit small. Sobolev-type error estimates when the target function is less smooth than functions in the native space developed in this paper. Michael M. Pahirya (Mukachevo)