Maximal Order and Order of Information for Numerical Quadrature

Abstract

The problem is to find approximataons [formula omitted] to the integral [formula omitted] The approximation as said to have “local order” [formula omitted] Methods are considered for computing such approximations which use “information” about f For fixed information, methods having maximal order are sought The main result is that the maximal order of any method using fixed mformauon as equal to the “order of the information,” as defined by Woźnlakowski This result is used to show that the maximal order for any method using the information [formula omitted]. © 1979, ACM. All rights reserved.