A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
In this paper,we investigate the{P,Q,k+1}-reflexive and anti-reflexive solutions to the system of matrix equations AX=C,XB=D and AXB=E.We present the necessary and sufficient conditions for the system men-tioned above...In this paper,we investigate the{P,Q,k+1}-reflexive and anti-reflexive solutions to the system of matrix equations AX=C,XB=D and AXB=E.We present the necessary and sufficient conditions for the system men-tioned above to have the{P,Q,k+1}-reflexive and anti-reflexive solutions.We also obtain the expressions of such solutions to the system by the singular value decomposition.Moreover,we consider the least squares{P,Q,k+1}-reflexive and anti-reflexive solutions to the system.Finally,we give an algorithm to illustrate the results of this paper.展开更多
The accuracy of parameter estimation is critical when digitally modeling a ship. A parameter estimation method with constraints was developed, based on the variational method. Performance functions and constraint equa...The accuracy of parameter estimation is critical when digitally modeling a ship. A parameter estimation method with constraints was developed, based on the variational method. Performance functions and constraint equations in the variational method are constructed by analyzing input and output equations of the system. The problem of parameter estimation was transformed into a problem of least squares estimation. The parameter estimation equation was analyzed in order to get an optimized estimation of parameters based on the Lagrange multiplication operator. Simulation results showed that this method is better than the traditional least squares estimation, producing a higher precision when identifying parameters. It has very important practical value in areas of application such as system identification and parameter estimation.展开更多
The anisotropic properties of subsurface media cause waveform distortions in seismic wave propagation,resulting in a negative infl uence on seismic imaging.In addition,wavefields simulated by the conventional coupled ...The anisotropic properties of subsurface media cause waveform distortions in seismic wave propagation,resulting in a negative infl uence on seismic imaging.In addition,wavefields simulated by the conventional coupled pseudo-acoustic equation are not only aff ected by SV-wave artifacts but are also limited by anisotropic parameters.We propose a least-squares reverse time migration(LSRTM)method based on the pure q P-wave equation in vertically transverse isotropic media.A fi nite diff erence and fast Fourier transform method,which can improve the effi ciency of the numerical simulation compared to a pseudo-spectral method,is used to solve the pure q P-wave equation.We derive the corresponding demigration operator,migration operator,and gradient updating formula to implement the LSRTM.Numerical tests on the Hess model and field data confirm that the proposed method has a good correction eff ect for the travel time deviation caused by underground anisotropic media.Further,it signifi cantly suppresses the migration noise,balances the imaging amplitude,and improves the imaging resolution.展开更多
This paper proposes the least-squares Galerkin finite dement scheme to solve secona-oraer hyperbolic equations. The convergence analysis shows that the method yields the approximate solutions with optimal accuracy in ...This paper proposes the least-squares Galerkin finite dement scheme to solve secona-oraer hyperbolic equations. The convergence analysis shows that the method yields the approximate solutions with optimal accuracy in （L2 （Ω））2 × L2 （Ω） norms. Moreover, the method gets the approximate solutions with second-order accuracy in time increment. A numerical example testifies the efficiency of the novel scheme. Key words Convergence analysis, Galerkin finite element, hyperbolic equations, least-squares, nu- merical example.展开更多
With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS a...With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS approximation leads to the development of the improved element-free Galerkin (IEFG) method. In this paper, the IEFG method is applied to study the partial differential equations that control the heat flow in three-dimensional space. With the IEFG technique, the Galerkin weak form is employed to develop the discretized system equations, and the penalty method is applied to impose the essential boundary conditions. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the transient heat conduction equations and the boundary and initial conditions are time dependent, the scaling parameter, number of nodes and time step length are considered in a convergence study.展开更多
文摘A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
基金supported by the National Natural Science Foundation of China(11571220)
文摘In this paper,we investigate the{P,Q,k+1}-reflexive and anti-reflexive solutions to the system of matrix equations AX=C,XB=D and AXB=E.We present the necessary and sufficient conditions for the system men-tioned above to have the{P,Q,k+1}-reflexive and anti-reflexive solutions.We also obtain the expressions of such solutions to the system by the singular value decomposition.Moreover,we consider the least squares{P,Q,k+1}-reflexive and anti-reflexive solutions to the system.Finally,we give an algorithm to illustrate the results of this paper.
基金Supported by the Navy Equipment Department Foundation under Grant No. 2009(189)
文摘The accuracy of parameter estimation is critical when digitally modeling a ship. A parameter estimation method with constraints was developed, based on the variational method. Performance functions and constraint equations in the variational method are constructed by analyzing input and output equations of the system. The problem of parameter estimation was transformed into a problem of least squares estimation. The parameter estimation equation was analyzed in order to get an optimized estimation of parameters based on the Lagrange multiplication operator. Simulation results showed that this method is better than the traditional least squares estimation, producing a higher precision when identifying parameters. It has very important practical value in areas of application such as system identification and parameter estimation.
基金financially supported by the National Key R&D Program of China (No. 2019YFC0605503)the Major Scientific and Technological Projects of CNPC (No. ZD2019-183-003)the National Natural Science Foundation of China (No. 41922028,41874149)。
文摘The anisotropic properties of subsurface media cause waveform distortions in seismic wave propagation,resulting in a negative infl uence on seismic imaging.In addition,wavefields simulated by the conventional coupled pseudo-acoustic equation are not only aff ected by SV-wave artifacts but are also limited by anisotropic parameters.We propose a least-squares reverse time migration(LSRTM)method based on the pure q P-wave equation in vertically transverse isotropic media.A fi nite diff erence and fast Fourier transform method,which can improve the effi ciency of the numerical simulation compared to a pseudo-spectral method,is used to solve the pure q P-wave equation.We derive the corresponding demigration operator,migration operator,and gradient updating formula to implement the LSRTM.Numerical tests on the Hess model and field data confirm that the proposed method has a good correction eff ect for the travel time deviation caused by underground anisotropic media.Further,it signifi cantly suppresses the migration noise,balances the imaging amplitude,and improves the imaging resolution.
基金This research is supported by the Mathematical Tianyuan Foundation of China under Grant No. 10726032, the National Natural Science Foundation of China under Grant No. 10471099, and the Fundamental Research Funds for the Central Universities.
文摘This paper proposes the least-squares Galerkin finite dement scheme to solve secona-oraer hyperbolic equations. The convergence analysis shows that the method yields the approximate solutions with optimal accuracy in （L2 （Ω））2 × L2 （Ω） norms. Moreover, the method gets the approximate solutions with second-order accuracy in time increment. A numerical example testifies the efficiency of the novel scheme. Key words Convergence analysis, Galerkin finite element, hyperbolic equations, least-squares, nu- merical example.
基金the National Natural Science Foundation of China (Grant No. 11171208)Shanghai Leading Academic Discipline Project (Grant No. S30106)
文摘With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS approximation leads to the development of the improved element-free Galerkin (IEFG) method. In this paper, the IEFG method is applied to study the partial differential equations that control the heat flow in three-dimensional space. With the IEFG technique, the Galerkin weak form is employed to develop the discretized system equations, and the penalty method is applied to impose the essential boundary conditions. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the transient heat conduction equations and the boundary and initial conditions are time dependent, the scaling parameter, number of nodes and time step length are considered in a convergence study.
