The least-square solutions of inverse problem for anti-symmetric and skew-symmetric matrices are studied. In addition, the problem of using anti-symmetric and skew-symmetric matrices to construct the optimal approxima...The least-square solutions of inverse problem for anti-symmetric and skew-symmetric matrices are studied. In addition, the problem of using anti-symmetric and skew-symmetric matrices to construct the optimal approximation to a given matrix is discussed, the necessary and sufficient conditions for the problem are derived, and the expression of the solution is provided. A numerical example is given to show the effectiveness of the proposed method.展开更多
By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution ^-X, which is both a least-sq...By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution ^-X, which is both a least-squares symmetric orthogonal anti-symmetric solu- tion of the matrix equation A^TXA = B and a best approximation to a given matrix X^＊. Moreover, a numerical algorithm for finding this optimal approximate solution is described in detail, and a numerical example is presented to show the validity of our algorithm.展开更多
In this paper,we prove the existence of general Cartesian vector solutions u=b(t)+A(t)x for the Ndimensional compressible Navier–Stokes equations with density-dependent viscosity,based on the matrix and curve integra...In this paper,we prove the existence of general Cartesian vector solutions u=b(t)+A(t)x for the Ndimensional compressible Navier–Stokes equations with density-dependent viscosity,based on the matrix and curve integration theory.Two exact solutions are obtained by solving the reduced systems.展开更多
文摘The least-square solutions of inverse problem for anti-symmetric and skew-symmetric matrices are studied. In addition, the problem of using anti-symmetric and skew-symmetric matrices to construct the optimal approximation to a given matrix is discussed, the necessary and sufficient conditions for the problem are derived, and the expression of the solution is provided. A numerical example is given to show the effectiveness of the proposed method.
基金The Project supported by Scientific Research Fund of Hunan Provincial Education Department,by National Natural Science Foundation of China (10171031)by Natural Science Fundation of Hunan Province (03JJY6028).
文摘By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution ^-X, which is both a least-squares symmetric orthogonal anti-symmetric solu- tion of the matrix equation A^TXA = B and a best approximation to a given matrix X^＊. Moreover, a numerical algorithm for finding this optimal approximate solution is described in detail, and a numerical example is presented to show the validity of our algorithm.
基金supported by NSFC(No.11271043,No.11471186)NSF of Beijing(No.1162002)the postdoctoral research foundation of Capital Normal University(No.043175606800/021)
基金This research is partially supported by the National Science Foundation of China(Grant No.11271079,10671095)RG 11/2015-2016R from the Education University of Hong Kong。
文摘In this paper,we prove the existence of general Cartesian vector solutions u=b(t)+A(t)x for the Ndimensional compressible Navier–Stokes equations with density-dependent viscosity,based on the matrix and curve integration theory.Two exact solutions are obtained by solving the reduced systems.
