Before revision:  Furthermore, the approximant is shown to be smooth and of approximation order of O(h^{m+1}) for non-noisy data , where h is the mesh size with respect to the manifold domain, and m is the degree of a local polynomial approximation utilized in our algorithm.
After revision:  Furthermore, the approximant is shown to be smooth and of approximation order of O(h^{m+1}) for non-noisy data , where h is the mesh size with respect to the manifold domain, and m is the degree of a local polynomial approximation , used in our algorithm.