Through the real representations of quaternion matrices and matrix rank method, we give the expression of the real ma-trices in least-squares g-inverse and minimum norm g-inverse. From these formulas, we derive the ex...Through the real representations of quaternion matrices and matrix rank method, we give the expression of the real ma-trices in least-squares g-inverse and minimum norm g-inverse. From these formulas, we derive the extreme ranks of the real matrices. As applications, we establish necessary and sufficient conditions for some special least-squares g-inverse and minimum norm g-inverse.展开更多
Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are...Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.展开更多
Based on the stability criteria of workpiece-fixture system, quantitative optimization of clamping forces during precise machining process for thin walled part is studied considering the contact condition between wokp...Based on the stability criteria of workpiece-fixture system, quantitative optimization of clamping forces during precise machining process for thin walled part is studied considering the contact condition between wokpiece and locator, the contact mechanical model is achieved, which is further been used to calculate the entire passive forces acting on the statically undetermined workpiece by means of the force screw theory as well as minimum norm force principle. Furthermore, a new methodology to optimize clamping forces is put forward, on the criteria of keeping the stability of workpiece during cutting process. By this way, the intensity of clamping forces is decreased dramatically, which will be most beneficial for improving the machining quality of thin-walled parts. Finally, a case study is used to support and validate the proposed model.展开更多
This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obt...This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.展开更多
It is a challenging issue to obtain the minimum amplitude control for linear systems subject to amplitudebounded disturbances.The difficulty is how to accurately give the quantitative relationship between the system H...It is a challenging issue to obtain the minimum amplitude control for linear systems subject to amplitudebounded disturbances.The difficulty is how to accurately give the quantitative relationship between the system H∞norm and control parameters.An optimal-Lyapunov-function-based controller design concept is proposed,and a minimum amplitude control scheme is presented under amplitude-bounded disturbances.Firstly,the optimal Lyapunov function is proposed by analyzing the geometric characteristics of the system H∞norm,and the necessary and sufficient condition of the optimal Lyapunov function parameter matrix is given.Secondly,the optimal Lyapunov function parameter matrix is constructed in the parameterized matrix equation,and the accurate quantitative relationship between the system H∞norm and control parameters is given.Finally,the control parameter optimization method is proposed according to the quantitative relationship between the system H∞norm and control parameters.Unlike robust optimization control methods,the presented minimum amplitude control scheme avoids the improper selection of the Lyapunov function in the controller design,and provides a novel way to design the minimum amplitude control under the given control accuracy.A buck converter example is given to illustrate the effectiveness and practicability of the presented scheme.展开更多
A novel fast algorithm for electrical capacitance tomography (ECT) was presented.The minimum norm solution was improved according to the nature of the inverse problems of ECT, and the stability of the numerical soluti...A novel fast algorithm for electrical capacitance tomography (ECT) was presented.The minimum norm solution was improved according to the nature of the inverse problems of ECT, and the stability of the numerical solution for the improvement was proved via the singular value decomposition principle.Some equations for further improvement of the reconstructed image were deduced by numerical optimization.Numerical experiments indicated that the improvement was efficient and the time of image reconstruction was similar to that of linear back-projection (LBP), however, the quality of the reconstructed image is better than other image reconstruction algorithms such as LBP, Tikhonov and Landweber algorithm.展开更多
文摘Through the real representations of quaternion matrices and matrix rank method, we give the expression of the real ma-trices in least-squares g-inverse and minimum norm g-inverse. From these formulas, we derive the extreme ranks of the real matrices. As applications, we establish necessary and sufficient conditions for some special least-squares g-inverse and minimum norm g-inverse.
文摘Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.
基金Beijing Municipal Commission of Education Project(XK100070530)
文摘Based on the stability criteria of workpiece-fixture system, quantitative optimization of clamping forces during precise machining process for thin walled part is studied considering the contact condition between wokpiece and locator, the contact mechanical model is achieved, which is further been used to calculate the entire passive forces acting on the statically undetermined workpiece by means of the force screw theory as well as minimum norm force principle. Furthermore, a new methodology to optimize clamping forces is put forward, on the criteria of keeping the stability of workpiece during cutting process. By this way, the intensity of clamping forces is decreased dramatically, which will be most beneficial for improving the machining quality of thin-walled parts. Finally, a case study is used to support and validate the proposed model.
基金This project is supported by the National Natural Science Foundation of China
文摘This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.
基金supported in part by the National Natural Science Foundation of China(62373089).
文摘It is a challenging issue to obtain the minimum amplitude control for linear systems subject to amplitudebounded disturbances.The difficulty is how to accurately give the quantitative relationship between the system H∞norm and control parameters.An optimal-Lyapunov-function-based controller design concept is proposed,and a minimum amplitude control scheme is presented under amplitude-bounded disturbances.Firstly,the optimal Lyapunov function is proposed by analyzing the geometric characteristics of the system H∞norm,and the necessary and sufficient condition of the optimal Lyapunov function parameter matrix is given.Secondly,the optimal Lyapunov function parameter matrix is constructed in the parameterized matrix equation,and the accurate quantitative relationship between the system H∞norm and control parameters is given.Finally,the control parameter optimization method is proposed according to the quantitative relationship between the system H∞norm and control parameters.Unlike robust optimization control methods,the presented minimum amplitude control scheme avoids the improper selection of the Lyapunov function in the controller design,and provides a novel way to design the minimum amplitude control under the given control accuracy.A buck converter example is given to illustrate the effectiveness and practicability of the presented scheme.
文摘A novel fast algorithm for electrical capacitance tomography (ECT) was presented.The minimum norm solution was improved according to the nature of the inverse problems of ECT, and the stability of the numerical solution for the improvement was proved via the singular value decomposition principle.Some equations for further improvement of the reconstructed image were deduced by numerical optimization.Numerical experiments indicated that the improvement was efficient and the time of image reconstruction was similar to that of linear back-projection (LBP), however, the quality of the reconstructed image is better than other image reconstruction algorithms such as LBP, Tikhonov and Landweber algorithm.
