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

2019/08/02 by Yousef Saad, Saad, Yousef · 3 citations
Computer Science · Mathematics · #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1908.01083

openalex publication_date 2019/08/02 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

This paper presents a brief historical survey of iterative methods for\nsolving linear systems of equations. The journey begins with Gauss who\ndeveloped the first known method that can be termed iterative. The early 20th\ncentury saw good progress of these methods which were initially used to solve\nleast-squares systems, and then linear systems arising from the discretization\nof partial different equations. Then iterative methods received a big impetus\nin the 1950s - partly because of the development of computers. The survey does\nnot attempt to be exhaustive. Rather, the aim is to underline the way of\nthinking at a specific time and to highlight the major ideas that steered the\nfield.\n

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