Mathematical Sciences: Block, Parallel and Nested Iterative Methods

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This research will study convergence properties and implementation details for several types of iterative methods for solving systems of linear equations on sequential computers and on the BBN Butterfly parallel computer. It will examine ways to dynamically determine the number of inner iterations that should be taken in a "nested iterative method," and provide convergence conditions for such methods. Block chaotic algoritms will also be investigated. The question of distributing the computational load in a parallel computing environment is crucial. The proposed research should give insight on this issue.