Error Estimates for the Solution of Linear Systems
Claude Brezinski · SIAM Journal on Scientific Computing · 1999
Let Ax=b be a system of linear equations where A is a square and nonsingular matrix. When solving it by a direct or an iterative method, an approximate solution x * is obtained (x * denotes the current iterate in the case of an iterative method). In this paper, we propose estimates for the norm of the error e=x-x * . These estimates are valid for any nonsingular matrix and for approximations x * of x obtained by any method and, thus, they also implicitly take into account the effect of rounding errors.