A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. Th...A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. The perturbation upper bounds of the solution are given for both the consistent and inconsistent cases. The obtained preturbation upper bounds are with respect to the distance from the perturbed solution to the unperturbed manifold.展开更多
In this article, the generalized reflexive solution of matrix equations （AX = B, XC = D） is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solv...In this article, the generalized reflexive solution of matrix equations （AX = B, XC = D） is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.展开更多
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
We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix（ATM） method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris ...We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix（ATM） method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation,which can be used to calculate the energies of higher rotational states from the energies of lower states.The energies of rotational states of the hydrogen molecule are calculated by the ATM condition,and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.展开更多
文摘A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. The perturbation upper bounds of the solution are given for both the consistent and inconsistent cases. The obtained preturbation upper bounds are with respect to the distance from the perturbed solution to the unperturbed manifold.
基金supported by National Natural Science Foundation of China (10571047)and by Scientific Research Fund of Hunan Provincial Education Department of China Grant(06C235)+1 种基金by Central South University of Forestry and Technology (06Y017)by Specialized Research Fund for the Doctoral Program of Higher Education (20060532014)
文摘In this article, the generalized reflexive solution of matrix equations （AX = B, XC = D） is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.
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Project supported by the Fund from the Science and Technology Committee of Shanghai Municipality,China (Grant No. 11ZR1412300)the National Natural Science Foundation of China (Grant No. 61108010)
文摘We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix（ATM） method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation,which can be used to calculate the energies of higher rotational states from the energies of lower states.The energies of rotational states of the hydrogen molecule are calculated by the ATM condition,and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.
