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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The minimum norm projection on $ C\sp{2}$-manifolds in $ {\bf R}\sp{n}$


Author: Theagenis J. Abatzoglou
Journal: Trans. Amer. Math. Soc. 243 (1978), 115-122
MSC: Primary 58C20; Secondary 41A50
MathSciNet review: 502897
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Abstract: We study the notion of best approximation from a point $ x \in {R^n}$ to a $ {C^2}$-manifold. Using the concept of radius of curvature, introduced by J. R. Rice, we obtain a formula for the Fréchet derivative of the minimum norm projection (best approximation) of $ x \in {R^n}$ into the manifold. We also compute the norm of this derivative in terms of the radius of curvature.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0502897-6
PII: S 0002-9947(1978)0502897-6
Article copyright: © Copyright 1978 American Mathematical Society