A Posteriori Error Bounds for Gaussian Elimination

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Abstract
Explicit bounds are constructed for the error in the solution of a system of linear algebraic equations obtained by Gaussian elimination using floating-point arithmetic. The bounds take account of inherent errors in the data and all abbreviations (choppings or roundings) introduced during the process of solution. The bounds are strict and agree with the estimate for the maximum error obtained by linearized perturbation theory. The formulation of the bounds avoids the need for specially directed rounding procedures in the hardware or software; in consequence the bounds can be evaluated on most existing computers. The cost of computing the bounds is comparable with the cost of computing the original solution.

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