Best local approximation in several variables
The problem of best local approximation in \(R^ n\) is studied. It is proved, in particular, that if V is a \(C^{m+1}\) subspace which is uniquely interpolating at 0 of order m, then the best local approximant from V to any function f which is \(C^{m+1}\) at 0 exists and is uniquely determined by matching all derivatives up through order m with those of f at 0. An analogous result on quasi-rational approximation is also obtained.
scientific article; zbMATH DE number 3873930