A Parallel Adaptive Gauss-Jordan Algorithm

This paper presents a parallel adaptive version of the block-based Gauss-Jordan algorithm, utilized to invert large matrices. This version includes a characterization of the workload and a mechanism of its folding/unfolding. Furthermore, this paper proposes a work scheduling strategy and an application-oriented solution for the fault tolerance problem. The application is implemented and experimented with MARS¹ in dedicated and non-dedicated environments. The results show that an absolute efficiency of 92% is possible on a cluster of DEC/ALPHA processors interconnected by a Gigaswitch network and an absolute efficiency of 67% can be obtained on an Ethernet network of SUN-Sparc 4 workstations. Moreover, the algorithm is tested on a meta-system including both the two parks of machines. Finally, an out-of-core solution for the algorithm is proposed. This solution allows a gain of 66% of data input operations and reduces the central memory space required for storing the data space of the algorithm by a factor q, where q is the dimension of the matrix to be inverted in terms of data blocks.