We propose a projection-type algorithm for generalized mixed variational in- equality problem in Euclidean space Rn. We establish the convergence theorem for the pro- posed algorithm, provided the multi-valued mapping...We propose a projection-type algorithm for generalized mixed variational in- equality problem in Euclidean space Rn. We establish the convergence theorem for the pro- posed algorithm, provided the multi-valued mapping is continuous and f-pseudomonotone with nonempty compact convex values on dom（f）, where f ： Rn --RU{＋∞} is a proper func- tion. The algorithm presented in this paper generalize and improve some known algorithms in literatures. Preliminary computational experience is also reported.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
In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator...In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator, we prove some strong convergence theorems of a new modified Halpern type hybrid iterative algorithm for the totally quasi-G-asymptotically nonexpansive semigroups in Banach space. The results presented in this paper extend and improve some corresponding ones by many others.展开更多
Although many effective algorithms of the gradient projection type have been given, there exist some problems which are not solved in these algorithms. In this paper, we consider the problem with nonlinear equality an...Although many effective algorithms of the gradient projection type have been given, there exist some problems which are not solved in these algorithms. In this paper, we consider the problem with nonlinear equality and inequality constraints and have given a generalized gradient projection algorithm. The global convergence of the algorithm has been proved and the problems have been solved completely by our algorithm.展开更多
This Letter proposes to apply full-color computer-generated holograms to the virtual image projection system so that the viewers can comfortably view floating images. Regarding the spatial division and distribution op...This Letter proposes to apply full-color computer-generated holograms to the virtual image projection system so that the viewers can comfortably view floating images. Regarding the spatial division and distribution operation,a modified Gerchberg–Saxton algorithm is used for acquiring the phase infographics, which are input into the spatial light modulator for the reconstructed projection. Such a virtual image projection system could reach the vertical angle of view of 15°–75° and the horizontal angle of view 360°, and the mixed-light modulating proportion contains a 3 m W red light laser, a 2 m W green light laser, and a 2.6 m W blue light laser to achieve the full-color mixed-light proportion with a speckle contrast of 6.65%. The relative diffraction efficiency and root mean square error of the reconstructed image are 95.3% and 0.0524, respectively.展开更多
基金supported by the Scientific Research Foundation of Sichuan Normal University(20151602)National Natural Science Foundation of China(10671135,61179033)and the Key Project of Chinese Ministry of Education(212147)
文摘We propose a projection-type algorithm for generalized mixed variational in- equality problem in Euclidean space Rn. We establish the convergence theorem for the pro- posed algorithm, provided the multi-valued mapping is continuous and f-pseudomonotone with nonempty compact convex values on dom（f）, where f ： Rn --RU{＋∞} is a proper func- tion. The algorithm presented in this paper generalize and improve some known algorithms in literatures. Preliminary computational experience is also reported.
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In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator, we prove some strong convergence theorems of a new modified Halpern type hybrid iterative algorithm for the totally quasi-G-asymptotically nonexpansive semigroups in Banach space. The results presented in this paper extend and improve some corresponding ones by many others.
基金the National Natural Science Foundation of China
文摘Although many effective algorithms of the gradient projection type have been given, there exist some problems which are not solved in these algorithms. In this paper, we consider the problem with nonlinear equality and inequality constraints and have given a generalized gradient projection algorithm. The global convergence of the algorithm has been proved and the problems have been solved completely by our algorithm.
基金supported by the National Science Council of Taiwan,China under contract NSC 101-2628-E-224-002-MY3
文摘This Letter proposes to apply full-color computer-generated holograms to the virtual image projection system so that the viewers can comfortably view floating images. Regarding the spatial division and distribution operation,a modified Gerchberg–Saxton algorithm is used for acquiring the phase infographics, which are input into the spatial light modulator for the reconstructed projection. Such a virtual image projection system could reach the vertical angle of view of 15°–75° and the horizontal angle of view 360°, and the mixed-light modulating proportion contains a 3 m W red light laser, a 2 m W green light laser, and a 2.6 m W blue light laser to achieve the full-color mixed-light proportion with a speckle contrast of 6.65%. The relative diffraction efficiency and root mean square error of the reconstructed image are 95.3% and 0.0524, respectively.
