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

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 firs...

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Bibliographic Details
Published in:International journal of computer mathematics 2018-02, Vol.95 (2), p.427-443
Main Authors: Beik, Fatemeh Panjeh Ali, Ahmadi-Asl, Salman, Ameri, Arezo
Format: Article
Language:English
Subjects:
Conditioning
Convergence
Economic models
Iterative method
Iterative methods
iterative refinement
Mathematical analysis
projection technique
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Summary: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.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2017.1290436