Geometry Algebra and Gauss Elimination method for solving a linear system of equations without division

Abstract

This paper aims to calculate the Gaussian elimination method without division operation, which is useful for cases where the division operation is considerably expensive, not optimised or inconvenient. To substitute the division, more multiplication steps are performed. The division is completely avoided, reaching only 7 % longer execution time on a modern computer. Memory savings and also less multiplication has been reached in comparison to the state-of-the-art approach.