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On the smoothness of best $ L\sb{2}$ approximants from nonlinear spline manifolds

Authors: Charles K. Chui, Philip W. Smith and Joseph D. Ward
Journal: Math. Comp. 31 (1977), 17-23
MSC: Primary 41A15
MathSciNet review: 0422955
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Abstract: Let $ S_n^k$ be the nonlinear spline manifold of order k and with n - k interior variable knots. We prove that all best $ {L_2}[0,1]$ approximants from $ S_n^k$ to a continuous function on [0, 1] are also continuous there. We also prove that there exists a $ {C^\infty }[0,1]$ function with no $ {C^2}[0,1]$ best $ {L_2}[0,1]$ approximants from $ S_n^k$.

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Article copyright: © Copyright 1977 American Mathematical Society

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