## The Exact Solution of Linear Equation Systems on a Shared Memory Multiprocessor (1992)

Venue: | In Submitted to the PARLE 93 |

Citations: | 3 - 3 self |

### BibTeX

@TECHREPORT{Schreiner92theexact,

author = {Wolfgang Schreiner and Volker Stahl},

title = {The Exact Solution of Linear Equation Systems on a Shared Memory Multiprocessor},

institution = {In Submitted to the PARLE 93},

year = {1992}

}

### OpenURL

### Abstract

We describe the design of a parallel algorithm for the exact solution of linear equation systems with integer coefficients and the implementation of this algorithm on a shared memory multiprocessor. An efficient solution of the original problem is difficult since the coefficients grow during the computation and arithmetic becomes very time-consuming. Therefore we transform the problem into a problem of determinant computation and apply a modular approach: the system is mapped into several finite fields where the determinants can be efficiently computed. The subresults are combined to yield the original determinants and to compute the solutions of the system. Several parallel versions of this algorithm have been developed and implemented on a shared memory multiprocessor. The programs are applied to equation systems of different characteristics and the results are analyzed and compared. Keywords: Parallel algorithms, scientific computing, computer algebra, shared memory machines. Fund...

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