Linear-system residual
= Linear-system residual
{title2=$r=b-Ax$}
The residual of an approximate solution $x$ of $Ax=b$ is $r=b-Ax$. It is the unbalanced right-hand side, while the solution error is $x_*-x=A^{-1}r$. The <Conjugate gradient method> makes residuals orthogonal to successive <Krylov subspaces>.