Conjugate gradient algorithm for fuzzy system of linear equations

Authors:
Zhou Guangming;Gan Yunzhi
Affiliations:
School of Mathematics and Computational Science, Xiangtan University, Xiangtan, P.R. China;School of Mathematics and Computational Science, Xiangtan University, Xiangtan, P.R. China
Venue:
FSKD'09 Proceedings of the 6th international conference on Fuzzy systems and knowledge discovery - Volume 4
Year:
2009

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Abstract

Fuzzy system of linear equations(FSLE) comes from many fields, including mathematics, physics, engineering and so on. It is an interesting work to study numerical methods solving the system. In this article, an conjugate gradient algorithm is presented for solving the FSLE. First, the system is translated into an equivalent unconstrained minimization problem(UMP). Then, an conjugate gradient algorithm is applied to solve the UMP. Finally, numerical results are given to illustrate the efficiency of the algorithm. The new algorithm for solving the FSLE converges to the exact solution of the system only after finite iterations. The algorithm is always valid whether the system matrix is symmetric or not, and its iterative numbers are less than ones gotten by using the existent steepest descent algorithm.