Parallel Processing Architecture for Solving Large Scale Linear Systems

Solving linear systems with multiple variables is at the core of many scienti…c problems. Parallel processing techniques for solving such system problems has have received much attention in recent years. A key theme in the literature pertains to the application of Lower triangular matrix and Upper triangular matrix(LU) decomposing, which factorizes an N N square matrix into two triangular matrices. The resulting linear system can be more easily solved in O(N²) work. Inher- ently, the computational complexity of LU decomposition is O(N³). Moreover, it is a challenging process to parallelize. A highly-parallel methodology for solving large-scale, dense, linear systems is proposed in this thesis by means of the novel application of Cramer’s Rule. A numerically stable scheme is described, yielding an overall computational complexity of O(N) with N² processing units.