[1]顾 颖,葛志利,陈 新.求解一类模糊线性系统的全局FOM和GMRES方法[J].南京师大学报(自然科学版),2021,44(01):13-19.[doi:10.3969/j.issn.1001-4616.2021.01.003]
　Gu Ying,Ge Zhili,Chen Xin.Global FOM and GMRES Methods for Solvinga Class of Fuzzy Linear Systems[J].Journal of Nanjing Normal University(Natural Science Edition),2021,44(01):13-19.[doi:10.3969/j.issn.1001-4616.2021.01.003]
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求解一类模糊线性系统的全局FOM和GMRES方法()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第44卷
期数:
2021年01期
页码:
13-19
栏目:
·数学·
出版日期:
2021-03-15

文章信息/Info

Title:
Global FOM and GMRES Methods for Solvinga Class of Fuzzy Linear Systems
文章编号:
1001-4616(2021)01-0013-07
作者:
顾 颖1; 葛志利2; 陈 新3
(1.宿迁学院文理学院,江苏 宿迁 223800)(2.南京科技职业学院基础科学部,江苏 南京 210048)(3.南京师范大学数学科学学院,江苏 南京 210023)
Author(s):
Gu Ying1; Ge Zhili2; Chen Xin3
(1.School of Literature and Science,Suqian College,Suqian 223800,China)(2.Basic Sciences Department,Nanjing Polytechnic Institute,Nanjing 210048,China)(3.School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China)
关键词:
模糊线性系统; 矩阵方程; 全局完全正交化方法; 全局广义极小残量法
Keywords:
fuzzy linear systems; matrix equation; global full orthogonalization method; global generalized minimum residual method
分类号:
O241.6
DOI:
10.3969/j.issn.1001-4616.2021.01.003
文献标志码:
A
摘要:
考虑一类n×n阶模糊线性系统,其系数矩阵是精确数矩阵,右端项为模糊数向量. 本文基于矩阵方程模型,提出求解该系统的全局完全正交化方法和全局广义极小残量法,并给出了收敛性分析. 最后,数值结果验证了新方法的稳定性与有效性.
Abstract:
In this paper,we consider a class of n×n fuzzy linear systems,whose coefficient matrix is an exact number matrix and the right-hand side is a fuzzy number vector. Based on the matrix equation model,we propose the global full orthogonalization method and the global generalized minimum residual method to solve the fuzzy linear systems. We also prove the convergence. Finally,numerical results illustrate the stability and effectiveness of the proposed methods.

参考文献/References:

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[9]王世恒,焦克莹. 模糊线性系统的新迭代方法[J]. 云南大学学报(自然科学版),2016,38(1):66-69.
[10]巩增泰,杨甲荣. 基于LR-梯形模糊数的模糊线性系统解问题及其数值计算[J]. 云南大学学报(自然科学版),2018,40(5):836-847.
[11]DUBOIS D,PRADE H.The mean value of a fuzzy number[J]. Fuzzy sets and systems,1987,24(3):279-300.
[12]SAAD Y,SCHULTZ M H.GMRES:a generalized minimal residual algorithm for solving nonsymmetric linear systems[J]. Society industry and applied mathematics journal on scientific computing,1986,7(3):856-869.
[13]JBILOU K,MESSAOUDI A,SADOK H.Global FOM and GMRES algorithms for matrix equation[J]. Applied numerical mathematics,1999,31(2):49-63.

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备注/Memo

备注/Memo:
收稿日期:2019-11-17.
基金项目:国家自然科学基金资助项目(11271196、12001281)、江苏省高校自然科学研究面上项目(17KJD110003)、江苏省高职院校教师专业带头人高端研修项目和江苏省青蓝工程资助项目.
通讯作者:陈新,博士,副教授,研究方向:数值线性代数. E-mail:chenxin2907@126.com
更新日期/Last Update: 2021-03-15