Let P∈C^(n×n)be a Hermitian and{k+1}-potent matrix,i.e.,P^(k+1)=P=P^(*),where(·)^(*)stands for the conjugate transpose of a matrix.A matrix X∈C^(n×n)is called{P,k+1}-reflexive(anti-reflexive)if PXP=X(...Let P∈C^(n×n)be a Hermitian and{k+1}-potent matrix,i.e.,P^(k+1)=P=P^(*),where(·)^(*)stands for the conjugate transpose of a matrix.A matrix X∈C^(n×n)is called{P,k+1}-reflexive(anti-reflexive)if PXP=X(P XP=-X).The system of matrix equations AX=C,XB=D subject to{P,k+1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases:k=1 and k=2,the least squares solution and the associated optimal approximation problem are also considered.展开更多
In this paper,we investigate the{P,Q,k+1}-reflexive and anti-reflexive solutions to the system of matrix equations AX=C,XB=D and AXB=E.We present the necessary and sufficient conditions for the system men-tioned above...In this paper,we investigate the{P,Q,k+1}-reflexive and anti-reflexive solutions to the system of matrix equations AX=C,XB=D and AXB=E.We present the necessary and sufficient conditions for the system men-tioned 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.展开更多
Let P∈C^(m×m)and Q∈C^(n×n)be Hermitian and{k+1}-potent matrices,i.e.,P k+1=P=P∗,Qk+1=Q=Q∗,where(·)∗stands for the conjugate transpose of a matrix.A matrix X∈C m×n is called{P,Q,k+1}-reflexive(an...Let P∈C^(m×m)and Q∈C^(n×n)be Hermitian and{k+1}-potent matrices,i.e.,P k+1=P=P∗,Qk+1=Q=Q∗,where(·)∗stands for the conjugate transpose of a matrix.A matrix X∈C m×n is called{P,Q,k+1}-reflexive(anti-reflexive)if P XQ=X(P XQ=−X).In this paper,the least squares solution of the matrix equation AXB=C subject to{P,Q,k+1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases:k=1 and k=2.展开更多
针对耦合神经P系统利用脉冲机制实现区域生长依赖于初始种子点选择的问题,提出一种自适应区域生长耦合神经P系统(adaptive region growing coupled neural P systems,ARGCNP)的图像分割方法。该方法利用金豺优化算法(golden jackal opti...针对耦合神经P系统利用脉冲机制实现区域生长依赖于初始种子点选择的问题,提出一种自适应区域生长耦合神经P系统(adaptive region growing coupled neural P systems,ARGCNP)的图像分割方法。该方法利用金豺优化算法(golden jackal optimization,GJO)的全局搜索能力,通过引入四种策略提升GJO的全局寻优性能,从而在图像中寻找最佳阈值点,以优化区域生长中的种子点选择。在实验中,首先通过CEC2017测试函数对改进后的GJO进行性能测试,结果表明改进后的GJO在测试函数上整体性能第一;随后将ARGCNP应用于分割彩色图像和医学图像,以峰值信噪比等三个指标对分割效果进行量化评价,分割结果显示该方法能够提升分割精度及分割结果的稳定性,证明ARGCNP在应用场景下具有的优势,能够满足图像分割需求。展开更多
基金Supported by the Education Department Foundation of Hebei Province(QN2015218)Supported by the Natural Science Foundation of Hebei Province(A2015403050)
文摘Let P∈C^(n×n)be a Hermitian and{k+1}-potent matrix,i.e.,P^(k+1)=P=P^(*),where(·)^(*)stands for the conjugate transpose of a matrix.A matrix X∈C^(n×n)is called{P,k+1}-reflexive(anti-reflexive)if PXP=X(P XP=-X).The system of matrix equations AX=C,XB=D subject to{P,k+1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases:k=1 and k=2,the least squares solution and the associated optimal approximation problem are also considered.
基金supported by the National Natural Science Foundation of China(11571220)
文摘In this paper,we investigate the{P,Q,k+1}-reflexive and anti-reflexive solutions to the system of matrix equations AX=C,XB=D and AXB=E.We present the necessary and sufficient conditions for the system men-tioned 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.
基金Supported by the Education Department Foundation of Hebei Province(Grant No.QN2015218).
文摘Let P∈C^(m×m)and Q∈C^(n×n)be Hermitian and{k+1}-potent matrices,i.e.,P k+1=P=P∗,Qk+1=Q=Q∗,where(·)∗stands for the conjugate transpose of a matrix.A matrix X∈C m×n is called{P,Q,k+1}-reflexive(anti-reflexive)if P XQ=X(P XQ=−X).In this paper,the least squares solution of the matrix equation AXB=C subject to{P,Q,k+1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases:k=1 and k=2.
文摘针对耦合神经P系统利用脉冲机制实现区域生长依赖于初始种子点选择的问题,提出一种自适应区域生长耦合神经P系统(adaptive region growing coupled neural P systems,ARGCNP)的图像分割方法。该方法利用金豺优化算法(golden jackal optimization,GJO)的全局搜索能力,通过引入四种策略提升GJO的全局寻优性能,从而在图像中寻找最佳阈值点,以优化区域生长中的种子点选择。在实验中,首先通过CEC2017测试函数对改进后的GJO进行性能测试,结果表明改进后的GJO在测试函数上整体性能第一;随后将ARGCNP应用于分割彩色图像和医学图像,以峰值信噪比等三个指标对分割效果进行量化评价,分割结果显示该方法能够提升分割精度及分割结果的稳定性,证明ARGCNP在应用场景下具有的优势,能够满足图像分割需求。
