On the iterative refinement of the solution of ill-conditioned linear system of equations

Fatemeh Panjeh Ali Beik, Salman Ahmadi-Asl, Arezo Ameri

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

Recently, Salkuyeh and Fahim [A new iterative refinement of the solution of ill-conditioned linear system of equations, Int. Comput. Math. 88(5) (2011), pp. 950–956] have proposed a two-step iterative refinement of the solution of an ill-conditioned linear system of equations. In this paper, we first present a generalized two-step iterative refinement procedure to solve ill-conditioned linear system of equations and study its convergence properties. Afterward, it is shown that the idea of an orthogonal projection technique together with a basic stationary iterative method can be utilized to construct a new efficient and neat hybrid algorithm for solving the mentioned problem. The convergence of the offered hybrid approach is also established. Numerical examples are examined to demonstrate the feasibility of proposed algorithms and their superiority to some of existing approaches for solving ill-conditioned linear system of equations.

Original languageEnglish
Pages (from-to)427-443
Number of pages17
JournalInternational Journal of Computer Mathematics
Volume95
Issue number2
DOIs
Publication statusPublished - 1 Feb 2018
Externally publishedYes

Keywords

  • convergence
  • Iterative method
  • iterative refinement
  • projection technique

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