Numerical Integration IV

Algorithms for the numerical computation of definite integrals have been proposed for more than 300 years, but practical considerations have led to problems of ever-increasing complexity, so that , even with current computing speeds, numerical integration may be a difficult task. High dimension and complicated structure of the region of integration and singularities of the integrand are the main sources of difficulties. This volume contains 27 papers presented at the fourth conference on numerical integration held at the Mathematical Research Institute, Oberwolfach, in November 1992. The contributions give a survey of the latest results in quadrature and cubature. Since the subject matter lies somewhere between practical mathematics and analysis, a wide spectrum of topics is discussed. One main theme is the construction of rules, especially for integrands with singularities. Further focal points are error estimation in various classes of functions, structure of general rules of interpolatory type, lattice rules, and the many facets of the Gaussian rule. Many open problems were discussed in Oberwolfach, showing a liveliness and actuality of the theory.
Nine of these problems could be given precise formulations; they are collected at the end of this volume.