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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58C20, 41A50

Retrieve articles in all journals with MSC: 58C20, 41A50

Additional Information

Article copyright: © Copyright 1978 American Mathematical Society