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Solving linear systems with a large number of variables is at the core of many scientific problems. Parallel processing techniques for solving such systems have received much attention in recent years. A pivotal theme in the literature pertains to the application of LU decomposing which factorizes an N×N square matrix in to two triangular matrices so that the resulting linear system can be more easily solved in O(N^2) work. Inherently, the computational complexity of LU decomposition is O(N^2). Moreover, it is a process that is challenging to parallelize. My work focuses on a highly-parallel methodology for solving large-scale, dense, linear systems by means of a novel application of Cramer's Rule. |
the university of tennessee
