CUBIC SPLINES WITH MINIMAL NORM*


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Abstract

Natural cubic interpolatory splines are known to have a minimal L2-norm of its second derivative on the C2 (or W22) class of interpolants. We consider cubic splines which minimize some other norms (or functionals) on the class of interpolatory cubic splines only. The cases of classical cubic splines with defect one (interpolation of function values) and of Hermite C1 splines (interpolation of function values and first derivatives) with spline knots different from the points of interpolation are discussed.

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