These papers were presented at the workshop on High Performance Computing and Gigabit Wide Area Networks held in September 1998 in Essen, Germany. The aim of the workshop was to analyse the interplay between computer network technology, communication software and the performance of mathematical algorithms used for large scale computations in wide area high speed computer networks. Only through interdisciplinary research with the co-operation of electrical engineers, mathematicians and computer scientists will it be possible to determine the most efficient combinations of parallel algorithms,...