Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub&...Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub>n</sub>}, derived from {A<sub>n</sub>}, which has also A aslimit and whose convergence is faster than the of {A<sub>n</sub>}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {A<sub>n</sub>} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is展开更多
The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions fo...The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions for the existence of such solutions and their general forms are derived.展开更多
In this paper, a system of complex matrix equations was studied. Necessary and sufficient conditions for the existence and the expression of generalized bipositive semidefinite solution to the system were given. In ad...In this paper, a system of complex matrix equations was studied. Necessary and sufficient conditions for the existence and the expression of generalized bipositive semidefinite solution to the system were given. In addition, a criterion for a matrix to be generalized bipositive semidefinite was determined.展开更多
Artificial neural network is a new approach to pattern recognition and classification. The model of multilayer perceptron （MLP） and back-propagation （BP） is used to train the algorithm in the artificial neural net...Artificial neural network is a new approach to pattern recognition and classification. The model of multilayer perceptron （MLP） and back-propagation （BP） is used to train the algorithm in the artificial neural network. An improved fast algorithm of the BP network was presented, which adopts a singular value decomposition （SVD） and a generalized inverse matrix. It not only increases the speed of network learning but also achieves a satisfying precision. The simulation and experiment results show the effect of improvement of BP algorithm on the classification of the surface defects of steel plate.展开更多
In late December of 1991, observation of three component geomagnetic short period variations was carried out in Chengmai county of Hainan province, along a short measurement profile with small spatial intervals of d...In late December of 1991, observation of three component geomagnetic short period variations was carried out in Chengmai county of Hainan province, along a short measurement profile with small spatial intervals of detection points. Within the period range of 20 s to 500 s, we have discovered that the vertical variations are basically correlated with the horizontal variations in north direction in all measurement points, the real parts of complex transfer functions demonstrate that an asymmetric spatial variation of short wavelength superimposed on regional monotonic tendencious spatial variation. Inversion of the observed data along the small profile was carried out by using the invention method of generalized inverse matrix of finite element forward calculation for the electromagnetic induction of the 2 D conductivity model to investigate the conductivity structure of the profile. We conclude that the anomaly of geomagnetic short periodic variation in the small area originated from the Wangwu Wenjiao fault in the northern part of Hainan island .展开更多
基金The works is supported by the National Natural Science Foundation of China(19871054)
文摘Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub>n</sub>}, derived from {A<sub>n</sub>}, which has also A aslimit and whose convergence is faster than the of {A<sub>n</sub>}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {A<sub>n</sub>} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is
文摘The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions for the existence of such solutions and their general forms are derived.
基金Project supported by the National Natural Science Foundation of China （Grant No.60672160）
文摘In this paper, a system of complex matrix equations was studied. Necessary and sufficient conditions for the existence and the expression of generalized bipositive semidefinite solution to the system were given. In addition, a criterion for a matrix to be generalized bipositive semidefinite was determined.
基金Item Sponsored by National Natural Science Foundation of China (60277029)
文摘Artificial neural network is a new approach to pattern recognition and classification. The model of multilayer perceptron （MLP） and back-propagation （BP） is used to train the algorithm in the artificial neural network. An improved fast algorithm of the BP network was presented, which adopts a singular value decomposition （SVD） and a generalized inverse matrix. It not only increases the speed of network learning but also achieves a satisfying precision. The simulation and experiment results show the effect of improvement of BP algorithm on the classification of the surface defects of steel plate.
文摘In late December of 1991, observation of three component geomagnetic short period variations was carried out in Chengmai county of Hainan province, along a short measurement profile with small spatial intervals of detection points. Within the period range of 20 s to 500 s, we have discovered that the vertical variations are basically correlated with the horizontal variations in north direction in all measurement points, the real parts of complex transfer functions demonstrate that an asymmetric spatial variation of short wavelength superimposed on regional monotonic tendencious spatial variation. Inversion of the observed data along the small profile was carried out by using the invention method of generalized inverse matrix of finite element forward calculation for the electromagnetic induction of the 2 D conductivity model to investigate the conductivity structure of the profile. We conclude that the anomaly of geomagnetic short periodic variation in the small area originated from the Wangwu Wenjiao fault in the northern part of Hainan island .
