Iterative Methods and Matrix Analysis (Computer Science)

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This research is aimed at analyzing and developing iterative methods for solving the nonsymmetric linear systems that arise in many areas of scientific computing. Current iterative methods for solving such problems ar sometimes effective but lack a firm theoretical foundation and may not be robust. Krylov space methods, such as GMRES, will be analyzed and the idea of choosing approximations from different spaces will also be considered. The biconjugate gradient and QMR algorithms will be related and an attempt made to explain their success. Potential for parallelism in various algorithms will be studied and parallel implementations will be developed for specific machine architectures. Collaborations are planned with Nick Trefethen and others in the Computer Science Department at Cornell. Two main activities for interacting with students are: teaching a graduate seminar ("CS 722") on iterative methods and matrix analysis, to familiarize students and other interested scientists and the state of the art in this field; and introducing a sophomore level practicum where, in conjunction with the numerical analysis course CS 222, students will implement parallel numerical algorithms on the machines available at the Cornell Theory Center. Various undergraduate seminars will be organized related to this activity.