A condensation-based application of Cramerʼs rule for solving large-scale linear systems

State-of-the-art software packages for solving large-scale linear systems are predominantly founded on Gaussian elimination techniques (e.g. LU-decomposition). This paper presents an efficient framework for solving large-scale linear systems by means of a novel utilization of Cramerʼs rule. While the latter is often perceived to be impractical when considered for large systems, it is shown that the algorithm proposed retains an O(N3)O(N3) complexity with pragmatic forward and backward stability properties. Empirical results are provided to substantiate the stated accuracy and computational complexity claims.