In the case of uniform grids, the error of the spline interpolant of a function defined on R has been well estimated. On the basis of the spline interpolation formula for functions defined on R we derive quasi‐interpolation formulae for functions defined on R or in a vicinity of a bounded interval, say [0,1], and we estimate the difference between the interpolant and the quasi‐interpolants.
Leetma, E., & Vainikko, G. (2007). Quasi‐interpolation by splines on the uniform knot sets. Mathematical Modelling and Analysis, 12(1), 107-120. https://doi.org/10.3846/1392-6292.2007.12.107-120
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