学术讲座【On global Hessenberg based methods for solving matrix equations】
时间：2018年6月16日(星期六)上午08:00-11:30
地点：理工北楼415
主办：数学与信息学院, 福建省分析数学及应用重点实验室
主讲：江夏学院，谢亚君教授
参加对象：相关专业老师及学生
专家简介：谢亚君，博士，江夏学院教授，研究方向为线性与非线性规划
报告摘要：In the talk, the use of Hessenberg-based methods for solving the Sylvester matrix equation AX + XB = C is investigated. To achieve this goal, the Sylvester form of the global generalized Hessenberg process is presented. Using this process, different methods based on a Petrov-Galerkin or on a minimal norm condition are derived. Meanwhile, The report focuses on the SGl-CMRH method which is based on the Sylvester form of the Hessenberg process with pivoting strategy combined with a minimal norm condition. In order to accelerate the SGl-CMRH method, a preconditioned framework of this method is also considered. It includes both fixed and flexible variants of the SGl-CMRH method. Moreover, the connection between the flexible preconditioned SGl-CMRH method and the fixed one is studied and some upper bounds for the residual norm are obtained. In particular, application of the obtained theoretical results is investigated for the special case of solving linear systems of equations with several right-hand sides. Finally, some numerical experiments are given in order to evaluate the effectiveness of the proposed methods.