  In large-scale applications including medical imaging, collocation
differential equation solvers, and estimation with differential privacy, the
underlying linear inverse problem can be reformulated as a streaming problem.
In theory, the streaming problem can be effectively solved using
memory-efficient, exponentially-converging streaming solvers. In practice, a
streaming solver's effectiveness is undermined if it is stopped before, or
well-after, the desired accuracy is achieved. In special cases when the
underlying linear inverse problem is finite-dimensional, streaming solvers can
periodically evaluate the residual norm at a substantial computational cost.
When the underlying system is infinite dimensional, streaming solver can only
access noisy estimates of the residual. While such noisy estimates are
computationally efficient, they are useful only when their accuracy is known.
In this work, we rigorously develop a general family of
computationally-practical residual estimators and their uncertainty sets for
streaming solvers, and we demonstrate the accuracy of our methods on a number
of large-scale linear problems. Thus, we further enable the practical use of
streaming solvers for important classes of linear inverse problems.
