An optimal interpolation formula with derivatives in Sobolev space
Keywords:
interpolation, splines, interpolation with derivatives, extremal function, error functionalAbstract
The construction of an optimal interpolation formula within the Hilbert space is the focus of this paper. The difference between a given function and an interpolation formula is estimated by the norm of the error functional. We use an extremal function for the error functional ???? in order to compute the norm. The interpolation formula’s coefficients and nodes affect the error functional. Here, with established nodes, the minimal value for the norm of the error functional is calculated with respect to coefficients. Encouraged, we obtain the system of linear equation for the optimal interpolation formula’s coefficients.
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