We shall consider two kinds of spline approximations over a uniform mesh. The first of them is mid-point spline interpolation and the second is histospline approximation. Our methods don't need any knowledge of derivative values, that is, end conditions are homogeneous ones dealing with function values. The linear systems for computing approximations may be conveniently and rapidly solved using the simple algorithm. Some numerical results are given which closely correspond with the prediction of the theory.
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Manabu Sakai, Riaz A. Usmani, Biquadratic Spline Approximations. Publ. Res. Inst. Math. Sci. 20 (1984), no. 3, pp. 431–446DOI 10.2977/PRIMS/1195181406