We discuss the incomplete semi-iterative method (ISIM) for an approximate solution of a linear fixed point equations x=Tx+c with a bounded linear operator T acting on a complex Banach space X such that its resolvent h...We discuss the incomplete semi-iterative method (ISIM) for an approximate solution of a linear fixed point equations x=Tx+c with a bounded linear operator T acting on a complex Banach space X such that its resolvent has a pole of order k at the point 1. Sufficient conditions for the convergence of ISIM to a solution of x=Tx+c, where c belongs to the range space of R(I-T) k, are established. We show that the ISIM has an attractive feature that it is usually convergent even when the spectral radius of the operator T is greater than 1 and Ind 1T≥1. Applications in finite Markov chain is considered and illustrative examples are reported, showing the convergence rate of the ISIM is very high.展开更多
Path planning in 3D geometry space is used to find an optimal path in the restricted environment, according to a certain evaluation criteria. To solve the problem of long searching time and slow solving speed in 3D pa...Path planning in 3D geometry space is used to find an optimal path in the restricted environment, according to a certain evaluation criteria. To solve the problem of long searching time and slow solving speed in 3D path planning, a modified ant colony optimization is proposed in this paper. Firstly, the grid method for environment modeling is adopted. Heuristic information is connected with the planning space. A semi-iterative global pheromone update mechanism is proposed. Secondly, the optimal ants mutate the paths to improve the diversity of the algorithm after a defined iterative number. Thirdly, co-evolutionary algorithm is used. Finally, the simulation result shows the effectiveness of the proposed algorithm in solving the problem of 3D pipe path planning.展开更多
基金Project1 990 1 0 0 6 supported by National Natural Science Foundation of China,Doctoral Foundation of China,Chi-na Scholarship council and Laboratory of Computational Physics in Beijing of Chinathe second author is also supportedby the State Major Key
文摘We discuss the incomplete semi-iterative method (ISIM) for an approximate solution of a linear fixed point equations x=Tx+c with a bounded linear operator T acting on a complex Banach space X such that its resolvent has a pole of order k at the point 1. Sufficient conditions for the convergence of ISIM to a solution of x=Tx+c, where c belongs to the range space of R(I-T) k, are established. We show that the ISIM has an attractive feature that it is usually convergent even when the spectral radius of the operator T is greater than 1 and Ind 1T≥1. Applications in finite Markov chain is considered and illustrative examples are reported, showing the convergence rate of the ISIM is very high.
基金Supported by National Natural Science Foundation of China (50875165)
文摘Path planning in 3D geometry space is used to find an optimal path in the restricted environment, according to a certain evaluation criteria. To solve the problem of long searching time and slow solving speed in 3D path planning, a modified ant colony optimization is proposed in this paper. Firstly, the grid method for environment modeling is adopted. Heuristic information is connected with the planning space. A semi-iterative global pheromone update mechanism is proposed. Secondly, the optimal ants mutate the paths to improve the diversity of the algorithm after a defined iterative number. Thirdly, co-evolutionary algorithm is used. Finally, the simulation result shows the effectiveness of the proposed algorithm in solving the problem of 3D pipe path planning.
