The area of research for this project is the iterative solution of large sparese linear systems of equations on vector and parallel computers. The goal of this research is to develop iterative algorithms which are adapted to parallel computers and which exploit the properties of parallel architectures. Three particular topics will be studied. First adaptive procedures for polynomial preconditioning of symmetric indefinite systems will be developed and tested. Second, research will be done on an adaptive polynomial method for solving nonsymmetric systems of equations for which the specturm of the matrix lies in an arbitrary region in the complex plane. A third topic of research will be the parallelization of restarted generalized conjugate gradient algorithms such as the GMRES algotithm. The goal of each of these topics of research is to develop algorithms which are better suited to highly parallel architectures.
