关于广义Sylvester矩阵方程反自反解的有限迭代算法  

On the finite iterative algorithm of anti-reflexive solution of generalized Sylvester matrix equation

作　　者：邓勇 DENG Yong(College of Mathematics and Statistics,Kashi University,Kashi 844006,China)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844006

出　　处：《东北师大学报（自然科学版）》2022年第1期34-43,共10页Journal of Northeast Normal University(Natural Science Edition)

基　　金：新疆维吾尔自治区自然科学基金资助项目(2016D01A014).

摘　　要：研究了广义Sylvester矩阵方程的广义反自反解,并给出了求其广义反自反解的一种新的有限迭代算法.通过此迭代法,可自动确定矩阵方程是否存在广义反自反解.此外,还讨论了给定矩阵基于Frobenius范数的近似解,从而推导出与给定广义Sylvester矩阵方程等价的矩阵方程的最佳逼近解.最后,用数值算例验证了该算法的有效性.The generalized anti-reflexive solution of generalized Sylvester matrix equation is studied and a new finite iterative algorithm to find its generalized anti-reflexive solution.By this iterative method, the existence of generalized anti-reflexive solutions for matrix equations can be determined automatically.In addition, nearest solution of a given matrix based on Frobenius norm is discussed, and the optimal approximation problem related to a given generalized Sylvester matrix equation is derived.Finally, the numerical example is used to verify the effectiveness of the algorithm.

关 键 词：广义Sylvester矩阵方程 有限迭代算法 反自反矩阵 最小Frobenius范数 最佳逼近解 

分 类 号：O241[理学—计算数学]