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:: Volume 9, Issue 4 (11-2019) ::
2019, 9(4): 49-54 Back to browse issues page
Proof of a conjecture of Yuan and Zontini on preconditioned methods for M-matrices
S. A. Edalatpanah , S. E. Najafi
Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran
Abstract:   (22 Views)
Systems of linear equations are ubiquitous in science and engineering, and iterative methods are indispensable for the numerical treatment of such systems. When we apprehend what properties of the coefficient matrix account for the rate of convergence, we may multiply the original system by some nonsingular matrix, called a preconditioner, so that the new coefficient matrix possesses better properties. Recently, some scholars presented several preconditioners and based on numerical tests proposed some conjectures for preconditioned iterative methods. In this paper, we prove one conjecture on the preconditioned Gauss–Seidel iterative method for solving linear systems whose coefficient matrix is an M-matrix.
Keywords: Iterative Methods, Preconditioning, Comparison Theorems, Spectral Radius, Conjecture, Gauss–Seidel, M-Matrix
Full-Text [PDF 541 kb]   (6 Downloads)    
Type of Study: Research | Subject: General
Received: 2019/05/12 | Accepted: 2019/08/24
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Edalatpanah S A, Najafi S E. Proof of a conjecture of Yuan and Zontini on preconditioned methods for M-matrices. International Journal of Applied Operational Research. 2019; 9 (4) :49-54
URL: http://ijorlu.liau.ac.ir/article-1-600-en.html


Volume 9, Issue 4 (11-2019) Back to browse issues page
ژورنال بین المللی پژوهش عملیاتی International Journal of Applied Operational Research - An Open Access Journal
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