ABSTRACT
Optimization plays an important role in solving systems of linear equations. In many applications the linear system is under-determined, meaning that there are multiple, indeed, infinitely many, solutions to the system. It is natural, then, to seek a solution that is optimal, in some sense. When the system involves measured data, as is often the case, there may be no exact solution, or an exact solution to the system may be too noisy. Then an approximate solution, or a solution to a related regularized system is sought. In this chapter we discuss briefly both of these situations, focusing on iterative algorithms that have been designed for such problems. For a more in-depth analysis of these problems see [59].
