Cubic interpolatory splines with nonuniform meshes (Q1066380)

Cubic spline interpolation problems of matching the spline at one intermediate point between the successive mesh points of a uniform mesh have been studied by \textit{A. Meir} and \textit{A. Sharma} [ibid. 1, 243-250 (1968)]. Further studies in this direction have been made by \textit{A. Chatterjee} and the first author [Proc. Am. Math. Soc. 82, 411-416 (1981; Zbl 0431.41011)]; the first author: [J. Approximation Theory 22, 105-110 (1978; Zbl 0386.41001)]; the first author and \textit{P. L. Powar} [ibid. 31, 99-106 (1981; Zbl 0482.41009)]. In the present paper existence, uniqueness and convergence properties of cubic spline interpolant matching at one intermediate point between the successive mesh points have been established for the case of a nonuniform mesh. Considering a geometric mesh it has also been shown that nonuniform meshes permit a wider choice for the points of interpolation than those possible for the case of uniform meshes.