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
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
Recently,the authors proposed a low-cost approach,named Optimization Approach for Linear Systems(OPALS)for solving any kind of a consistent linear system regarding the structure,characteristics,and dimension of the co...Recently,the authors proposed a low-cost approach,named Optimization Approach for Linear Systems(OPALS)for solving any kind of a consistent linear system regarding the structure,characteristics,and dimension of the coefficient matrix A.The results obtained by this approach for matrices with no structure and with indefinite symmetric part were encouraging when compare with other recent and well-known techniques.In this work,we proposed to extend the OPALS approach for solving the Linear Least-Squares Problem(LLSP)and the Minimum Norm Linear System Problem(MNLSP)using any iterative low-cost gradient-type method,avoiding the construction of the matrices AT A or AAT,and taking full advantage of the structure and form of the gradient of the proposed nonlinear objective function in the gradient direction.The combination of those conditions together with the choice of the initial iterate allow us to produce a novel and efficient low-cost numerical scheme for solving both problems.Moreover,the scheme presented in this work can also be used and extended for the weighted minimum norm linear systems and minimum norm linear least-squares problems.We include encouraging numerical results to illustrate the practical behavior of the proposed schemes.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.
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Recently,the authors proposed a low-cost approach,named Optimization Approach for Linear Systems(OPALS)for solving any kind of a consistent linear system regarding the structure,characteristics,and dimension of the coefficient matrix A.The results obtained by this approach for matrices with no structure and with indefinite symmetric part were encouraging when compare with other recent and well-known techniques.In this work,we proposed to extend the OPALS approach for solving the Linear Least-Squares Problem(LLSP)and the Minimum Norm Linear System Problem(MNLSP)using any iterative low-cost gradient-type method,avoiding the construction of the matrices AT A or AAT,and taking full advantage of the structure and form of the gradient of the proposed nonlinear objective function in the gradient direction.The combination of those conditions together with the choice of the initial iterate allow us to produce a novel and efficient low-cost numerical scheme for solving both problems.Moreover,the scheme presented in this work can also be used and extended for the weighted minimum norm linear systems and minimum norm linear least-squares problems.We include encouraging numerical results to illustrate the practical behavior of the proposed schemes.
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.
