Parallelism in algebraic computation and parallel algorithms for symbolic linear systems

Abstract

Parallel execution of algebraic computation is discussed in the first half of this paper. It is argued that, although a high efficiency is obtained by parallel execution of divide-and-conquer algorithms, the ratio of the throughput to the number of processors is still small. Parallel processing will be most successful for the modular algorithms and many algorithms in linear algebra. In the second half of this paper, parallel algorithms for symbolic determinants and linear equations are proposed. The algorithms manifest a very high efficiency in a simple parallel processing scheme. These algorithms are well usable in also the serial processing scheme.