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This paper presents a brief historical survey of iterative methods forsolving linear systems of equations. The journey begins with Gauss whodeveloped the first known method that can be termed iterative. The early 20thcentury saw good progress of these methods which were initially used to solveleast-squares systems, and then linear systems arising from the discretizationof partial different equations. Then iterative methods received a big impetusin the 1950s - partly because of the development of computers. The survey doesnot attempt to be exhaustive. Rather, the aim is to underline the way ofthinking at a specific time and to highlight the major ideas that steered thefield.

Iterative methods for linear systems of equations: A brief historical journey