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

Harika Bolledla¹؛ Rajaiah Dasari^{* 2}؛ Shivaji Arepelly¹؛ Ladalla Raj Kumar³

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

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

³Department of Mathematics, Kakatiya University, India

چکیده

In this article, the Triangular and Symmetric splitting iterative method is suggested for solving linear homogenous systems of equations $\pi Q=0$, where $Q$ is the stochastic rate matrix and $\pi$ is the steady state vector. The homogenous system is converted to the non-homogenous regularized fuzzy linear system $Ax=b$ with the small perturbation parameter $0 < r \leq 1$. The regularized fuzzy linear system is converted into an embedded linear system. The iterative scheme is established, and convergence criteria and its sensitivity analysis are analyzed using numerical examples and convergence 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