Kriterien zweiter Ordnung für lokal beste Approximationen

Consider the problem of approximating (in the Chebyshev-norm) a real-valued functionf(x) on a compact subsetX of ℝm,m≧1, by an element of a set of functionsa(p, x), p∈P,P⊆ ℝn an open set. Both necessary and sufficient conditions of the second order for ana(p0,x) to be a locally best approximation are derived. Apart from conditions on the differentiability off anda, onX, and on the error functionf(x)−a(p0,x) we impose no restrictions on the problem. This makes the results applicable to a broad class of problems