Backward error
= Backward error
{title2=$\delta d$}
A <backward error> measures a perturbation $\delta d$ of the input data for which the computed result is an exact solution of the perturbed problem. Specify which data may change and which <norm> measures the perturbation. For a <linear system> $A\widehat{x}=b$, holding $A$ fixed gives $\delta b=A\widehat{x}-b$, the negative <linear-system residual>. The corresponding <forward error> also depends on the <condition number>.