  This paper presents a brief historical survey of iterative methods for
solving linear systems of equations. The journey begins with Gauss who
developed the first known method that can be termed iterative. The early 20th
century saw good progress of these methods which were initially used to solve
least-squares systems, and then linear systems arising from the discretization
of partial different equations. Then iterative methods received a big impetus
in the 1950s - partly because of the development of computers. The survey does
not attempt to be exhaustive. Rather, the aim is to underline the way of
thinking at a specific time and to highlight the major ideas that steered the
field.
