The minimum norm projection on 𝐶²-manifolds in 𝑅ⁿ

Abstract

Abstract. We study the notion of best approximation from a point x £ R" to a C2-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 e R" into the manifold. We also compute the norm of this derivative in terms of the radius of curvature.