It has been known for at least five decades that control theory
can be used to study iterative algorithms. However, little work can be found
in the control systems literature on numerical algorithms, especially on the
study of finite precision effects. In this technical note, we consider numerical
iterative algorithms in finite precision as dynamical systems and study
the effects of finite precision using control theory. By using the control tools
of input-to-state stability and results from the study of quantization in control
systems, we present new systematic ways to find bounds on the forward
error for iterative algorithms. The advantages of the proposed schemes are
shown by applying them to find bounds for the classical iterative methods
for solving a system of linear equations.