Mathematical Sciences: Block, Parallel and Nested Iterative Methods

本研究将研究在顺序计算机和BBN Butterfly并行计算机上求解线性方程组的几种迭代方法的收敛性质和实现细节。它将研究动态确定“嵌套迭代方法”中应该采用的内部迭代次数的方法，并为此类方法提供收敛条件。块混沌算法也将被研究。在并行计算环境中分配计算负载的问题至关重要。拟议的研究应该对这个问题有深入的了解。

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.