On maximal order for local and global numerical problems

摘要

We consider algorithms using linear information to solve a linear local or global problem. Although adaptive nonlinear algorithms are possible, we show the existence of nonadaptive linear algorithms having maximal order among all methods using this information. In particular, this answers (in the affirmative) a conjecture made by the author that there always exist maximal-order methods for the local quadrature problem which are nonadaptive and linear.