The minimum norm projection on 𝐶²-manifolds in 𝑅ⁿ

Abatzoglou, Theagenis J.

doi:10.1090/S0002-9947-1978-0502897-6

The minimum norm projection on $C^{2}$-manifolds in $\textbf {R}^{n}$
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by Theagenis J. Abatzoglou

Trans. Amer. Math. Soc. 243 (1978), 115-122

DOI: https://doi.org/10.1090/S0002-9947-1978-0502897-6

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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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