The Experts below are selected from a list of 4044 Experts worldwide ranked by ideXlab platform
Yeong-cheng Liou - One of the best experts on this subject based on the ideXlab platform.
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strong convergence of a self adaptive method for the split feasibility problem
Fixed Point Theory and Applications, 2013Co-Authors: Yonghong Yao, Mihai Postolache, Yeong-cheng LiouAbstract:Self-adaptive methods which permit step-sizes being selected self-adaptively are effective methods for solving some important problems, e.g., variational inequality problems. We devote this paper to developing and improving the self-adaptive methods for solving the split feasibility problem. A new improved self-adaptive method is introduced for solving the split feasibility problem. As a special case, the Minimum Norm Solution of the split feasibility problem can be approached iteratively.
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strong convergence of a modified extragradient method to the Minimum Norm Solution of variational inequalities
Abstract and Applied Analysis, 2012Co-Authors: Muhammad Aslam Noor, Yeong-cheng LiouAbstract:We suggest and analyze a modified extragradient method for solving variational inequalities, which is convergent strongly to the Minimum-Norm Solution of some variational inequality in an infinite-dimensional Hilbert space.
Na Huang - One of the best experts on this subject based on the ideXlab platform.
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modified conjugate gradient method for obtaining the Minimum Norm Solution of the generalized coupled sylvester conjugate matrix equations
Applied Mathematical Modelling, 2016Co-Authors: Na HuangAbstract:Abstract In this study, we consider the iteration Solutions of the generalized coupled Sylvester-conjugate matrix equations: A 1 X + B 1 Y = D 1 X ¯ E 1 + F 1 , A 2 Y + B 2 X = D 2 Y ¯ E 2 + F 2 , where X ¯ and Y ¯ denote the conjugation of X and Y , respectively. We propose a modified conjugate gradient method and give the convergence analysis based on the premise that the coupled matrix equations are consistent. The convergence theorem shows that a Solution ( X * , Y * ) can be obtained within finite iterative steps in the absence of round-off error for any initial value. Furthermore, we provide a method for choosing the initial matrices to obtain the Minimum-Norm Solution of the problem. Finally, some numerical examples are given to demonstrate the behavior of the algorithms considered.
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the modified conjugate gradient methods for solving a class of generalized coupled sylvester transpose matrix equations
Computers & Mathematics With Applications, 2014Co-Authors: Na HuangAbstract:In this paper, we consider the iteration Solutions of generalized coupled Sylvester-transpose matrix equations: A1XB1+C1YTD1=F1, A2YB2+C2XTD2=F2. When the coupled matrix equations are consistent, we propose a modified conjugate gradient method to solve the equations and prove that a Solution (X∗,Y∗) can be obtained within finite iterative steps in the absence of roundoff-error for any initial value. Furthermore, we show that the Minimum-Norm Solution can be got by choosing a special kind of initial matrices. When the coupled matrix equations are inconsistent, we present another modified conjugate gradient method to find the least-squares Solution with the Minimum-Norm. Finally, some numerical examples are given to show the behavior of the considered algorithms.
Guoliang Chen - One of the best experts on this subject based on the ideXlab platform.
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A New Method for the Bisymmetric Minimum Norm Solution of the Consistent Matrix Equations
Journal of Applied Mathematics, 2013Co-Authors: Guoliang Chen, Xiangyun ZhangAbstract:We propose a new iterative method to find the bisymmetric Minimum Norm Solution of a pair of consistent matrix equations , . The algorithm can obtain the bisymmetric Solution with Minimum Frobenius Norm in finite iteration steps in the absence of round-off errors. Our algorithm is faster and more stable than Algorithm 2.1 by Cai et al. (2010).
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a new method for the bisymmetric Minimum Norm Solution of the consistent matrix equations a 1 xb 1 c 1 a 2 xb 2 c 2
Journal of Applied Mathematics, 2013Co-Authors: Guoliang Chen, Xiangyun ZhangAbstract:We propose a new iterative method to find the bisymmetric Minimum Norm Solution of a pair of consistent matrix equations , . The algorithm can obtain the bisymmetric Solution with Minimum Frobenius Norm in finite iteration steps in the absence of round-off errors. Our algorithm is faster and more stable than Algorithm 2.1 by Cai et al. (2010).
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an iterative method for the symmetric and skew symmetric Solutions of a linear matrix equation axb cyd e
Journal of Computational and Applied Mathematics, 2010Co-Authors: Xingping Sheng, Guoliang ChenAbstract:In this paper, two efficient iterative methods are presented to solve the symmetric and skew symmetric Solutions of a linear matrix equation AXB+CYD=E, respectively, with real pair matrices X and Y. By these two iterative methods, the solvability of the symmetric and skew symmetric Solutions for the matrix equation can be determined automatically. When the matrix equation has symmetric and skew symmetric Solutions, then, for any initial pair matrices X"0 and Y"0, symmetric and skew symmetric Solutions can be obtained within finite iteration steps in the absence of roundoff errors, and the Minimum Norm of the symmetric and skew symmetric Solutions can be obtained by choosing a special kind of initial pair matrices. In addition, the unique optimal approximation pair Solution X@^ and Y@^ to the given matrices X@? and Y@? in Frobenius Norm can be obtained by finding the Minimum Norm Solution of a new matrix equation AX@?B+CY@?D=E@?, where E@?=E-AX@?B-CY@?D. The given numerical examples demonstrate that the iterative methods are quite efficient.
Yijie Ren - One of the best experts on this subject based on the ideXlab platform.
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Regularization Method for the Approximate Split Equality Problem in Infinite-Dimensional Hilbert Spaces
Abstract and Applied Analysis, 2013Co-Authors: Rudong Chen, Yijie RenAbstract:We studied the approximate split equality problem (ASEP) in the framework of infinite-dimensional Hilbert spaces. Let , , and be infinite-dimensional real Hilbert spaces, let and be two nonempty closed convex sets, and let and be two bounded linear operators. The ASEP in infinite-dimensional Hilbert spaces is to minimize the function over and . Recently, Moudafi and Byrne had proposed several algorithms for solving the split equality problem and proved their convergence. Note that their algorithms have only weak convergence in infinite-dimensional Hilbert spaces. In this paper, we used the regularization method to establish a single-step iterative for solving the ASEP in infinite-dimensional Hilbert spaces and showed that the sequence generated by such algorithm strongly converges to the Minimum-Norm Solution of the ASEP. Note that, by taking in the ASEP, we recover the approximate split feasibility problem (ASFP).
Weifeng Zhao - One of the best experts on this subject based on the ideXlab platform.
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Inverse Kinematic Control of a Dual Crane System Experiencing Base Motion
IEEE Transactions on Control Systems Technology, 2015Co-Authors: Frank A. Leban, James Díaz-gonzalez, Gordon G Parker, Weifeng ZhaoAbstract:For over 30 years, many active and passive antipendulation concepts have been explored for use on cranes in the marine environment. These range from simple tension member restraints to command filtering strategies and advanced feedback control laws, where both measured ship/platform motion and payload swing are required. Single crane control systems that compensate for own ship or target ship motion and payload swing damping are well developed, and have been demonstrated. Cargo transfer control is more complex when multiple ship-mounted cranes are used, representing a closed kinematic chain. However, the potential benefits include larger capacity and better load control. In this brief, an inverse kinematic control strategy is presented that uses two cranes' actuation capability (hoist lengths and boom angles) to keep its load fixed in inertial space regardless of the motion of the ship on which the cranes are mounted. An underdetermined Solution is developed. Unique crane commands can then be computed using a Minimum Norm Solution. A dynamic simulation is described for use in algorithm development and initial validation. Final verification was performed using two cranes mounted on a motion controlled platform.