In recent years, there has been a great interest in large-scale and real-time matrix compu- tationsj these computations arise in a variety of fields, such as computer graphics, imaging, speech and image processing, telecommunication, biomedical signal processing, optimiza- tion and so on. This volume gives an account of recent research advances in numerical techniques used in large-scale and real-time computations and their implementation on high performance computers. For anyone interested in any of the aforementioned disci- plines, this collection of papers is of value and provides state-of-the-art expositions as weil as new and important trends and directions for the future, motivated and illustrated by a wealth of scientific and engineering applications. The volume is an outgrowth of the NATO Advanced Study Institute "Linear Algebra for Large-Scale and Real-Time Applications," held at Leuven, Belgium, August 1992. We were quite fortunate to be able to gather such an exceilent group of researchers to participate in this Institute. We are indebted to all the participants who enriched the meeting through their many contributions. Special thanks are due to the invited speakers at the Institute, P. Bjlifrstad, Universitetet i Bergen -Norway, S. Boyd, Stanford University -U. S. A., G. Cy- benko, Dartmouth College -U. S. A., J. Demmel, University of California Berkeley -U. S. A, E. Deprettere, Technische Universiteit Delft -The Netherlands, P. Dewilde, Technische Uni- versiteit Delft -The Netherlands, R. Freund, AT & T -U. S. A., M.