ar X iv : 1 50 6 . 07 38 7 v 4 [ m at h . C A ] 2 0 Se p 20 17 CARDINAL INTERPOLATION WITH GENERAL MULTIQUADRICS : CONVERGENCE RATES
نویسنده
چکیده
This article pertains to interpolation of Sobolev functions at shrinking lattices hZ from Lp shift-invariant spaces associated with cardinal functions related to general multiquadrics, φα,c(x) := (|x| + c). The relation between the shift-invariant spaces generated by the cardinal functions and those generated by the multiquadrics themselves is considered. Additionally, Lp error estimates in terms of the dilation h are considered for the associated cardinal interpolation scheme. This analysis expands the range of α values which were previously known to give such convergence rates (i.e. O(h) for functions with derivatives of order up to k in Lp, 1 < p < ∞). Additionally, the analysis here demonstrates that some known best approximation rates for multiquadric approximation are obtained by their cardinal interpolants.
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