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.
| Identifer | oai:union.ndltd.org:UTENN/oai:trace.tennessee.edu:utk_gradthes-1081 |
| Date | 01 August 2009 |
| Creators | Nagari, Arun |
| Publisher | Trace: Tennessee Research and Creative Exchange |
| Source Sets | University of Tennessee Libraries |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Masters Theses |
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