ABSTRACT
Given an n by n nonsingular matrix A and an n-vector b, the linear system A x = b can always be solved for x by Gaussian elimination. The work required is approximately 2n 3/3 operations (additions, subtractions, multiplications, and divisions), and, in general, n 2 words of storage are required. This is often acceptable if n is of moderate size, say n ≤ 1000, but for much larger values of n, say, n ≈ 106, both the work and storage for Gaussian elimination may become prohibitive.
