共查询到20条相似文献,搜索用时 15 毫秒
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Zhen-yunPeng Xi-yanHu LeiZhang 《计算数学(英文版)》2004,22(6):873-880
The necessary and sufficient conditions for the existence of and the expressions for the bisymmetric solutions of the matrix equations (Ⅰ)A1X1B1 A2X2B2 ^… AkXkBk=D,(Ⅱ)A1XB1 A2XB2 … AkXBk=D and (Ⅲ) (A1XB1,A2XB2,…,AkXBk)=(D1,D2,…,Dk) are derived by using Kronecker product and Moore-Penrose generalized inverse of matrices. In addition, in corresponding solution set of the matrix equations, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm is given. Numerical methods and numerical experiments of finding the neaxest solutions axe also provided. 相似文献
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讨论形如Xn+2-BXn+1-AXn=O,A,B,Xn为m阶矩阵的二阶齐次矩阵差分方程通解的表达式为Xn=C1Un1+C2Un2的充分或必要条件.主要的方法是利用矩阵差分方程的特征矩阵方程解的性质. 相似文献
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本文利用多项式的最大公因式给出的求r-循环矩阵和对称r-循环矩阵求逆的快速算法。该方法不需要计算三角函数并且具有很少的计算量。 相似文献
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矩阵方程AXC+BYD=E的解及其最佳逼近 总被引:1,自引:0,他引:1
本文利用矩阵的广义奇异值分解给出了矩阵方程AXC=BYD=E有解的充分必要条件及其通解的表达式,同时在矩阵方程的解集合中导出了与给定矩阵的最佳逼近解的表达式。 相似文献
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AnpingLiao ZhongzhiBai 《计算数学(英文版)》2003,21(2):175-182
Least-squares solution of AXB=D with respect to symmetric positive semidefinite matrix X is considered.By making use of the generalized singular value ecomposition,we derive general analytic formulas,and present necessary and sufficient conditions for guaranteeing the existence of the solution.By applying MATLAB 5.2,we give some numerical examples to show the feasibility and accuracy of this construciton technique in the finite precision arithmetic. 相似文献
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该文讨论了两类线性流形上矩阵方程B^TXB=D的反对称解和反对称最佳逼近解存在的条件,给出了通解的一般表达式,同时解决了解对给定矩阵的唯一最佳逼近问题. 相似文献
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矩阵方程ATXA=D的条件数与向后扰动分析 总被引:1,自引:0,他引:1
讨论矩阵方程ATXA=D,该方程源于振动反问题和结构模型修正.本文利用Moore-Penrose广义逆的性质,给出该方程解的条件数的上、下界估计.同时,利用Schauder不动点理论给出该方程的向后扰动界,这些结果可用于该矩阵方程的数值计算. 相似文献
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A System of Four Matrix Equations over von Neumann Regular Rings and Its Applications 总被引:3,自引:0,他引:3
QingWenWANG 《数学学报(英文版)》2005,21(2):323-334
We consider the system of four linear matrix equations A1X = C1, XB2=C2, A3XB3=C3 and A4XB4 = C4 over h, an arbitrary von Neumann regular ring with identity. A necessary and sufficient condition for the existence and the expression of the general solution to the system are derived. As applications, necessary and sufficient conditions are given for the system of matrix equations A1X = C1 and A3X=C3 to have a bisymmetric solution, the system of matrix equations A1X = C1 and A3XB3 = C3 to have a perselfconjugate solution over h with an involution and char h≠2, respectively. The representations of such solutions are also presented. Moreover, some auxiliary resultson other systems over h are obtained. The previous known results on some systems of matrix equations are special cases of the new results. 相似文献
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In this article we establish necessary and sufficient conditions for the existence and the expressions of the general real solutions to the classical system of quaternion matrix equations A 1 XB 1 = C 1, A 2 XB 2 = C 2. Moreover, formulas of the maximal and minimal ranks of four real matrices X 1, X 2, X 3, and X 4 in solution X = X 1 + X 2 i + X 3 j + X 4 k to the system mentioned above are derived. As applications, we give necessary and sufficient conditions for the quaternion matrix equations A 1 XB 1 = C 1, A 2 XB 2 = C 2, A 3 XB 3 = C 3 to have common real solutions. In addition, the maximal and minimal ranks of four real matrices E, F, G, and H in the common generalized inverse of A 1 + B 1 i + C 1 j + D 1 k and A 2 + B 2 i + C 2 j + D 2 k, which can be expressed as E + Fi + Gj + Hk are also presented. 相似文献
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讨论了二阶线性矩阵差分方程AXn+2+BXn+1+CXn=0的解及其渐近稳定性.首先,给出了它的特征方程有解的一个充要条件,然后利用特征方程两个相异的解刻划出该矩阵差分方程的通解,并分析其解的渐近稳定性,最后运用一实例验证了相关结果. 相似文献
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通过求极值的方法,得到了求矩阵方程AHXA=B与已知矩阵最佳逼近的反H erm ite-自反解的存在的充要条件. 相似文献
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矩阵方程组AX=C,XB=D的公共最小二乘解 总被引:1,自引:0,他引:1
通过使用矩阵秩方法,我们给出了矩阵方程组AX =C,XB =D的公共最小二乘解的通解表达式,以及公共最小二乘解的极大秩和极小秩. 相似文献
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利用四元数矩阵的广义Frobenius范数和弱圈积,建立一个关于四元数矩阵的实函数并简洁表征其极小值.再用四元数矩阵的奇异值分解和广义Frobenius范数的性质,讨论四元数矩阵方程组[AX,XB]=[C,D]的最小二乘解,得到了解的具体表达式.最后在该方程组的解集合中导出了与给定矩阵的最佳逼近解的表达式. 相似文献
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通过Hermite矩阵的谱分解及一个改进的Young不等式,得到了关于正定矩阵的两个不等式,所得结果是对一些经典的矩阵不等式的进一步推广.最后,作为应用,给出了著名的Holder不等式和Minkowsi不等式的一种反向形式. 相似文献
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设HF为域F上广义四元数可除代数,其中charF≠2.应用伴随矩阵与矩阵表示方法,本文得到HF上矩阵方程∑ki=0AiXBi=E有解或有唯一解的几个充要条件,并且给出了几个解的公式. 相似文献