Iterative solution of linear systems in the 20th century

Yousef Saad, Henk A. Van Der Vorst

Research output: Contribution to journalArticlepeer-review

337 Scopus citations


This paper sketches the main research developments in the area of iterative methods for solving linear systems during the 20th century. Although iterative methods for solving linear systems find their origin in the early 19th century (work by Gauss), the field has seen an explosion of activity spurred by demand due to extraordinary technological advances in engineering and sciences. The past five decades have been particularly rich in new developments, ending with the availability of large toolbox of specialized algorithms for solving the very large problems which arise in scientific and industrial computational models. As in any other scientific area, research in iterative methods has been a journey characterized by a chain of contributions building on each other. It is the aim of this paper not only to sketch the most significant of these contributions during the past century, but also to relate them to one another.

Original languageEnglish (US)
Pages (from-to)1-33
Number of pages33
JournalJournal of Computational and Applied Mathematics
Issue number1-2
StatePublished - Nov 1 2000


  • ADI
  • Krylov subspace methods
  • Multigrid
  • Polynomial acceleration
  • Preconditioning
  • Relaxation methods
  • SOR
  • Sparse approximate inverse


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