矩阵方程组的{P,Q,k+1}-自反解
厉洁;王卿文
【期刊名称】《应用数学与计算数学学报》 【年(卷),期】2024(032)003
【摘要】主要研究了矩阵方程组AX=C,XB=D,AXB=E的{P,Q,k+1}-自反解和反自反解.通过奇异值分解,得到了以上方程组有{P,Q,k+1}-自反解和反自反解的充要条件,并给出了解的表达式.更进一步地,考虑了一般情况下方程组的最小二乘{P,Q,k+1}-自反解和反自反解.最后,给出了一个算法,且通过两个算例验证了其有效性.%In this paper,we investigate the {P,Q,k + 1}-reflexive and antireflexive solutions to the system of matrix equations AX =C,XB =D and AXB =E.We present the necessary and sufficient conditions for the system mentioned above to have the {P,Q,k + 1}-reflexive and anti-reflexive solutions.We also obtain the expressions of such solutions to the system by the singular value decomposition.Moreover,we consider the least squares {P,Q,k + 1}-reflexive and anti-reflexive solutions to the system.Finally,we give an algorithm to illustrate the results of this paper. 【总页数】12页(619-630)
【关键词】矩阵方程;最小二乘解;{ P,Q,k+1}-(反)自反解;奇异值分解 【作者】厉洁;王卿文
【作者单位】上海大学理学院,上海200444;上海大学理学院,上海200444 【正文语种】中文 【中图分类】O151.26
矩阵方程组的{P,Q,k+1}-自反解
