Automatic approximation using asymptotically optimal adaptive interpolation

Abstract We present an asymptotic analysis of adaptive methods for L p approximation functions f ∈ C r ([ a , b ]), where $1\le p\le +\infty $ 1 ≤ p + ∞ . The rely on piecewise polynomial interpolation degree − 1 with strategy selecting m subintervals. optimal speed convergence is in this case order and it already achieved by the uniform (nonadaptive) subdivision initial interval; however, constant crucially depends chosen strategy. derive asymptotically best strategies show their applicability to automatic given accuracy ε