The cardinal interpolant of functions on the real line by splines is determined by certain formula free of solving large or infinite systems. We apply this formula to functions given on the interval [0,1] introducing special extensions of functions from [0,1] into the real line which maintains the optimal error estimates. The computation of the parameters determining the interpolant costs O (n log n) operations.
Vainikko, G. (2009). Cardinal approximation of functions by splines on an interval. Mathematical Modelling and Analysis, 14(1), 127-138. https://doi.org/10.3846/1392-6292.2009.14.127-138
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