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Abstract
Most spline interpolation operators such as the nodal spline operator introduced by de Villiers and Rohwer in 1987 interpolate data at spline knots. In this paper, we are going to present a method of how to construct a local spline interpolation operator that interpolates at sites that are different from the spline knots. These considerations result in the quasi-nodal spline interpolation operator of degree n that reproduces all polynomials of degree not exceeding n.
Notes
In order to be more transparent, we only omit the knots , in this definition.