I will describe how C*-algebras have been used to prove results in numerical analysis. Until recently, the results obtained were of a theoretical nature (e.g. C*-algebra theory would imply that certain vectors had to converge to a solution of some equation). However, I will discuss how some general theory can also be used to prove rates of convergence in a number of natural and important cases. Surprisingly some very specialized and highly technical work in operator algebras (e.g. an AF-embedding due to Pimsner and Voiculescu) plays a key role in obtaining explicit rates of convergence.