This conference was held at the Mathematical Research Institute in Oberwolfach from 30 November to 6 December 1986 under the direc tion of J. Albrecht (Clausthal-Zellerfeld), L. Collatz (Hamburg), W. Velte (Wlirzburg) and W. Wunderlich (Bochum). Focal points during the meeting were eigenvalue problems in the engineering sciences and in industry, methods for calculating bounds for eigenvalues, and matrix eigenvalue problems. Central to the lectures on eigenvalue problems pertinent to the engineering sciences and industry were oscillation and stability problems; for these, numerical treatment drew mainly on finite element methods in the lectures as well as in the ensuing discus sions, questions concerning the quality of the mathematical models applied, and the choice of appropriate finite elements, were given wide latitude. Other lectures addressed new research results in the calculation of (primarly lower) bounds for eigenvalues. The ramifications of these results were illustrated by numerous examples taken from fields in the engineering sciences and physics. The extensive use of finite-element methods (made possible in the wake of major computer advances) has led to new research in matrix eigenvalue problems, and several lectures reported on results which have been achieved in this area.

Inhalt
Anwendungen des Verfahrens von Lehmann auf Scbwingungsprobleme.- Einfluss der Modell- und Elementqualität auf die Berechnung der Eigenschwingungen dünnwandiger Konstruktionen mit der FEM.- Invariant Subspaces for T-invariant Operators.- Rapid Resolution of Truncated Intermediate Problems.- Analysis und Berechnung der Falk'schen ECP-Transformation und verwandte Probleme.- Eigenfrequencies Estimates for Structures with Non-Prismatic Elements.- Eigenvalue Problems of Vibrating Coupled Mechanical Structures Approximate Solutions and Experimental Results.- Ein Stufenverfahren zur Berechnung von Eigenwertschranken.- The Quantum Mechanical Two-Centre Coulomb Problem as a Check for the Accuracy of the Ritz Method and the Validity of Eckart's Inequality and its Generalization.- Computation of Eigenvalue and Eigenfunctions of Symmetric Operators by Defect-Minimization.- Zur Eigenwerteinschliessung bei nichtselbstadjungierten Eigenwertaufgaben mit Differentialgleichungen.- The Hybrid Dissolution of a Double Eigenvalue.- A Lanczos Algorithm with Restarts.- Zur Herleitung von Einschliessungssätzen für Eigenwerte.- Zur numerischen Behandlung von Instabilitäten in der Strukturdynamik.- An Iteration Method of Improving Computable Bounds for Eigenvalues.- Transverse Eigenmode Spectra of Opto-Couplers and Semiconductor Injection Laser Diodes.- Numerical Solution of the Navier-Stokes Equations Related to a Problem of Marangoni Convection.- A New Justification of Finite Dynamic Element Methods.