Parallel real-world LU decomposition: Gauss vs. Crout algorithm

This paper presents numerical experiments with assorted versions of parallel LU matrix decomposition algorithms (Gauss and Crout algorithm). The tests have been carried out on the hardware platform with four-core Skylake processor featuring hyperthreading technology doubling virtually core number. Parallelization algorithms have been implemented with the aid of classic POSIX threads library. Experiments have shown that basic 4-thread acceleration of all parallel implementations is almost equal to the number of threads/processors. Both algorithms are worth considering in real-world applications (Florida University collection). Gauss algorithm is a better performer, with respect to timing, in the case of matrices with lower density of nonzeros, as opposed to higher density matrices. The latter are processed more efficiently with the aid of Crout algorithm implementation.