Counterexamples in Optimal Quadrature

Werschulz, Arthur G.

It is widely believed that order of exactness is a good measure of the quality of an algorithm for numerical quadrature. We show that this is not the case, by exhibiting a situation in which the optimal algorithm does not even integrate constants exactly. We also show that there are situations in which the penalty for using equidistant nodes is unbounded. Finally, we show that the complexity of obtaining an ε-approximation can be an arbitrary function of ε, i.e., there is no hardest quadrature problem.


More About This Work

Academic Units
Computer Science
Department of Computer Science, Columbia University
Columbia University Computer Science Technical Reports, CUCS-067-83
Published Here
October 25, 2011