Error Estimates for the Solution of Linear Systems

Authors:
C. Brezinski
Affiliations:
-
Venue:
SIAM Journal on Scientific Computing
Year:
1999

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Abstract

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.