GAUSSIAN ELIMINATION

Gaussian elimination - A method to solve Ax=b that performs elementary row operations on A to annihilate successive elements of A in order to reduce A to an upper triangular matrix, U. On paper, the same operations are applied to b, then the solution is obtained by solving the resulting upper triangular system. In a computer, the product of the matrices effecting the elementary row operations is a lower triangular matrix, L, with unit diagonal. Once this phase is completed, the system Ax=b becomes LUx=b. This is then solved in two steps: forward substitution solves Ly=b; then backward substitution solves Ux=y. (Of course, computer implementations vary.) Here is a