Convergence analysis of triangular and symmetric splitting method for fuzzy stochastic linear systems

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 29 اسفند 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.91136.1561

نویسندگان

B. Harika¹؛ D. Rajaiah^{* 2}؛ A. Shivaji¹؛ L.P. Rajkumar¹

¹Department of Mathematics, Kakatiya University, Telangana, India.

²Department of Mathematics, Kakatiya Institute of Technology and Science, Warangal, India.

چکیده

In this article, the triangular and symmetric splitting iterative method is suggested for solving linear homogeneous systems of equations $πQ = 0$, where $Q$ is the stochastic rate matrix and π is the steady state vector. The homogeneous system is converted to the nonhomogeneous regularized fuzzy linear system $Ax = b$ with the small perturbation parameter $0 < r ≤ 1$. The regularized fuzzy linear system is converted into an embedded linear system. The iterative scheme is established; convergence criteria and its sensitivity analysis are analyzed using the numerical examples and conver-gence theorems. From the numerical results, it is evident to conclude that the proposed method is effective and efficient compared to the theoretical results.

کلیدواژه‌ها

Stochastic rate matrix؛ Triangular and symmetric splitting Method؛ Fuzzy liner system؛ Error analysis

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