This grant will partially support the Fourth IMACS International Symposium on Iterative Methods in Scientific Computation to be held October 18-20, l998, at the University of Texas at Austin. The symposium will be dedicated to providing an overview of the state of the art in the use of iterative methods for solving large sparse linear systems with an eye to contributions of the past, present, and future. The emphasis will be placed upon identifying current and future research directions in the mainstream of modern scientific computing. Of particular interest will be talks on interdisciplinary research, applications, and open problems.