The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory 1] held there from August 4-10, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirty-nine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem...

Das Mathematische Forschungsinstitut Oberwolfach veranstaltet seit langerer Zeit in etwa zweijahrigem Turnus Tagungen uber numerische Methoden der Approximationstheorie. Die Vortragsauszuge der diesjahrigen Tagung, die vom 13. bis 19. Juni stattfand, sind in dem vorliegenden Band zusammengefat. Die Themen lassen erkennen, da es ein besonderes Anliegen der Tagungsleiter war, die Kluft zwischen abstrakter Mathematik und den Anwendungen verringern zu helfen. Approximationstheoretische Fragestellungen scheinen geeignet zu sein, hier neue Bru ken zu schlagen. Der starke Zustrom auslandischer...

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.