Error control process in function interpolation using statistical spline model

In this paper, we propose an algebraic method based on solving some inequalities of polynomial type to control the error value of interpolation formulas whose residue depends on a monic polynomial. This method then leads to construct some piecewise approximations (splines) of statistical type, which are based on a specific partition of the main interval. In other words, in this model of spline, approximate criteria are considered fixed and sub-intervals corresponding to criteria are derived as accurately as possible. In this sense, some statistical concepts such as expected value, variance measure, skewness and kurtosis coefficients are also inserted into the definition of statistical splines. Finally, a numerical results section is separately given to confirm all results in the paper.