Optimal Nodes for Interpolatory Product Integration

Abstract

This paper is concerned with choices of nodes in numerical integration rules to evaluate (kf).Here k is any element of a normed space corresponding to some integrability requirement, and f is many times differentiable, conditions which are appropriate to the practical application of such rules. By examining the behaviour of the error functional it is shown how optimal nodes can be defined in these circumstances.For finite intervals and a variety of integrability conditions on k, the resulting optimal nodes are defined and compared. Further results, although less complete, are obtained for similar integrals over the whole of and over +.