International Journal of Applied Operational Research
ژورنال بین المللی پژوهش عملیاتی
International Journal of Applied Operational Research - An Open Access Journal
Basic Sciences
http://ijorlu.liau.ac.ir
1
admin
2251-6867
2251-9432
8
7
14
8888
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en
jalali
1398
8
1
gregorian
2019
11
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9
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online
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fulltext
en
Proof of a conjecture of Yuan and Zontini on preconditioned methods for M-matrices
عمومى
General
پژوهشي
Research
<span class="tlid-translation translation" lang="fa"><span title="">یوان و زونتینی چندین مدل از پیش شرط سازی با قضایای مقایسه را برای حل دستگاه های معادلات خطی معرفی کردند که ماتریس ضرایب آنها M- ماتریس است.</span> <span title="">علاوه بر این، بر اساس آزمایشات عددی ، آنها چند حدس را برای حل روش تکراری گاوس-سایدل پیش شرط سازی شده ارائه دادند.</span> <span title="">در این مقاله ، ما یک حدس ارائه شده را اثبات می کنیم.</span></span><br>
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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.
Iterative Methods, Preconditioning, Comparison Theorems, Spectral Radius, Conjecture, Gauss–Seidel, M-Matrix
49
54
http://ijorlu.liau.ac.ir/browse.php?a_code=A-10-446-4&slc_lang=en&sid=1
S. A.
Edalatpanah
saedalatpanah@gmail.com
10031947532846001225
10031947532846001225
Yes
Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran
S. E.
Najafi
e.najafi@aihe.ac.ir
10031947532846001226
10031947532846001226
No
Department of Industrial Engineering, Islamic Azad University, Central Tehran Branch, Tehran 14676-86831, Iran.