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J. Math. Mech. 15 (1966), pp. 953–970 On splines and their minimum properties

By Carl De Boor, Robert E. Lynch and Communicated G. Birkhoff


0. Introduction. It is the purpose of this note to show that the several minimum properties of odd degree polynomial spline functions [4, 18] all derive from the fact that spline functions are representers of appropriate bounded linear functionals in an appropriate Hilbert space. (These results were first announced in Notices, Amer. Math. Soc., 11 (1964) 681.) In particular, spline interpolation is a process of best approximation, i.e., of orthogonal projection, in this Hilbert space. This observation leads to a generalization of th

Year: 2014
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