基于降维的并行符号行列式计算

An Algorithm of Computing Symbolic Determinants Based on Dimension-decreasing

为了更有效地计算科学与工程领域所涉及的大量符号行列式计算,基于降维算法和并行行列式计算,呈现了一个混合的符号行列式计算算法。新算法将多变元的符号行列式转化为仅有两个变元的并行行列式计算。更重要的是,新算法大大提高了原并行算法的并行度。实验结果表明,新算法有效地减少了中间过程的膨胀,因此更能处理多变元的且阶数较高的符号行列式。

To efficiently compute the determinants of symbolic matrices arising in science and engineering fields, based on dimension-decreasing algorithm and parallel computation of symbolic determinant, a hybrid algorithm, which can convert the computation of a given multivariate determinant to the computation of a univariate determinant, was presented. In addition, the degree of parallelism was enhanced greatly. Experimental results showed that this new algorithm can effectively reduce the intermediate expression swell and deal with some symbolic determinants with polynomial entries in many variables.