Several kind of new numerical schemes for the stationary Navier-Stokes equations based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, togeth...Several kind of new numerical schemes for the stationary Navier-Stokes equations based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, together with their error estimations are presented. All these algorithms are constructed under an uniform frame, that is to construct some kind of new projections for the Sobolev space in which the true solution is sought. It is shown that the proposed inertial algorithms can greatly improve the convergence rate of the standard Galerkin approximate solution with lower computing effort. And some numerical examples are also given to verify results of this paper.展开更多
A new method is illustrated for processing the output of a set of triad orthogonal rate gyros and accelerometers to reconstruct vehicle navigation parameters(attitude, velocity, and position). The paper introduces two...A new method is illustrated for processing the output of a set of triad orthogonal rate gyros and accelerometers to reconstruct vehicle navigation parameters(attitude, velocity, and position). The paper introduces two vectors with dimensions 4×1 as velocity and position quaternions.The navigation equations for strapdown systems are nonlinear but after using these parameters, the navigation equations are converted into a pseudo-linear system. The new set of navigation equations has an analytical solution and the state transition matrix is used to solve the linear timevarying differential equations through time series. The navigation parameters are updated using the new formulation for strapdown navigation equations. Finally, the quaternions of velocity and position are converted into the original position and velocity vectors. The combination of the coning motion and a translational oscillatory trajectory is used to evaluate the accuracy of the proposed algorithm. The simulations show significant improvement in the accuracy of the inertial navigation system, which is achieved through the mentioned algorithm.展开更多
The problem of finding fixed points of nonexpansive mappings on Hadamard manifolds is considered in this paper.To solve this kind of problem,we propose a modified Riemannian Mann algorithm with inertial effect.Under t...The problem of finding fixed points of nonexpansive mappings on Hadamard manifolds is considered in this paper.To solve this kind of problem,we propose a modified Riemannian Mann algorithm with inertial effect.Under the assumption of existence of fixed points of the nonexpansive mapping,the global convergence of the proposed algorithm is established.To show the efficiency of the proposed algorithm,numerical comparisons with some existing algorithms are reported.展开更多
基金Subsidized by the Special Funds for Major State Basic Research ProjectsG1999032801-07,NSFC(10101020,10001028)Tian Yuan Funds(TY10126004)
文摘Several kind of new numerical schemes for the stationary Navier-Stokes equations based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, together with their error estimations are presented. All these algorithms are constructed under an uniform frame, that is to construct some kind of new projections for the Sobolev space in which the true solution is sought. It is shown that the proposed inertial algorithms can greatly improve the convergence rate of the standard Galerkin approximate solution with lower computing effort. And some numerical examples are also given to verify results of this paper.
文摘A new method is illustrated for processing the output of a set of triad orthogonal rate gyros and accelerometers to reconstruct vehicle navigation parameters(attitude, velocity, and position). The paper introduces two vectors with dimensions 4×1 as velocity and position quaternions.The navigation equations for strapdown systems are nonlinear but after using these parameters, the navigation equations are converted into a pseudo-linear system. The new set of navigation equations has an analytical solution and the state transition matrix is used to solve the linear timevarying differential equations through time series. The navigation parameters are updated using the new formulation for strapdown navigation equations. Finally, the quaternions of velocity and position are converted into the original position and velocity vectors. The combination of the coning motion and a translational oscillatory trajectory is used to evaluate the accuracy of the proposed algorithm. The simulations show significant improvement in the accuracy of the inertial navigation system, which is achieved through the mentioned algorithm.
基金the first author is supported by the Zhejiang Provincial Natural Science Foundation of China(Grant No.LY21A010004)the National Natural Science Foundation of China(Grant No.11701514)+2 种基金The research of the second author is supported by the research grants MYRG2019-00042-FST and CPG2023-00023-FST from University of MacaoThe research of the third author is supported by the Zhejiang Provincial Natural Science Foundation of China(Grant No.LY21A010010)the National Natural Science Foundation of China(Grant No.11601112).
文摘The problem of finding fixed points of nonexpansive mappings on Hadamard manifolds is considered in this paper.To solve this kind of problem,we propose a modified Riemannian Mann algorithm with inertial effect.Under the assumption of existence of fixed points of the nonexpansive mapping,the global convergence of the proposed algorithm is established.To show the efficiency of the proposed algorithm,numerical comparisons with some existing algorithms are reported.
