Parallel Gaussian elimination for banded matrix-a computational model

A parallel Gaussian elimination technique for the solution of a system of equations of the form Ax=C, where A is a banded matrix, is modeled as an acyclic directed graph. This graph is useful in the identification of parallel operations, the minimum absolute completion time for the solution process and the minimum number of processors required to solve it in minimum time. Hu´s (1961) level scheduling strategy is used for scheduling operations to processors. The absolute minimum completion time sets a limit on the speedup; it is dependent on the order of the A matrix and is independent of the bandwidth. The minimum number of processors required to complete the solution process is fixed by the bandwidth and is independent of the order of the A matrix. A method of incorporating communication aspects in between processors in four kinds of interconnections is also presented