Abstract
We extend results given by Zó and Cuenya in 2007 about a general approach to problems of best vector-valued approximation on small regions from a finite dimensional subspace of polynomials of some degree. This approach is called best local approximation. We consider a weighted local approximation of a vector-valued function on the origin and a weighted best local approximation of a real-valued function on several points, similar to classical problems in best local approximation with balanced neighborhood.
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