On the smoothness of best 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

DOI:
https://doi.org/10.1090/S0025-5718-1977-0422955-7

MathSciNet review:
0422955

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the nonlinear spline manifold of order *k* and with *n* - *k* interior variable knots. We prove that all best approximants from to a continuous function on [0, 1] are also continuous there. We also prove that there exists a function with no best approximants from .

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0422955-7

Article copyright:
© Copyright 1977
American Mathematical Society