  In the computational sciences, one must often estimate model parameters from
data subject to noise and uncertainty, leading to inaccurate results. In order
to improve the accuracy of models with noisy parameters, we consider the
problem of reducing error in a linear system with the operator corrupted by
noise. To address this problem, we extend the elliptic operator augmentation
framework (Etter, Ying 2020) to the general nonsymmetric matrix case. We show
that under the conditions of right-hand-side isotropy and noise symmetry that
the optimal operator augmentation factor for the residual error is always
positive, thereby making the framework amenable to a necessary bootstrapping
step. While the above conditions are unnecessary for positive optimal
augmentation factor in the elliptic case, we provide counter-examples that
illustrate their necessity when applied to general matrices. When the noise in
the operator is small, however, we show that the condition of noise symmetry is
unnecessary. Finally, we demonstrate through numerical experiments on Markov
chain problems that operator augmentation can significantly reduce error in
noisy matrix systems -- even when the aforementioned conditions are not met.
