en 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&nbsp; است.</span> <span title="">علاوه بر این، بر اساس آزمایشات عددی ، آنها چند حدس را برای حل روش تکراری&nbsp; گاوس-سایدل&nbsp;پیش شرط سازی شده&nbsp; ارائه دادند.</span> <span title="">در این مقاله ، ما یک حدس&nbsp; ارائه شده&nbsp; را اثبات می کنیم.</span></span><br> <br> &nbsp; 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&ndash;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.lahijan.iau.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.