Symbolic algorithm for solving comrade linear systems based on a modified Stair-Diagonal Approach

Recently, a new approach called Stair-Diagonal was used for solving a tridiagonal system by Jawad [A.J. Jawad, A. Yildirim, A. Biswas, Solving a tri-diagonal system of size N equations by Stair-Diagonal Approach, Adv. Sci. Eng. Med. 4 (2012) 171-175]. In this paper, we developed a Stair-Diagonal Approach in order to remove the cases where the Stair-Diagonal Approach fails. Also, we describe a symbolic computational algorithm for solving comrade linear systems based on a modified Stair-Diagonal Approach. The computational cost of our algorithm is O(n2). The algorithm is implementable to a Computer Algebra System (CAS) such as MAPLE, MATLAB and MATHEMATICA. Three examples are presented for the sake of illustration.