The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Lin Xiao - One of the best experts on this subject based on the ideXlab platform.
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a finite time convergent neural dynamics for online solution of time varying linear complex Matrix Equation
Neurocomputing, 2015Co-Authors: Lin XiaoAbstract:This paper proposes and investigates a finite-time convergent neural dynamics (FTCND) for online solution of time-varying linear complex Matrix Equation in complex domain. Different from the conventional gradient-based neural dynamical method, the proposed method utilizes adequate time-derivative information of time-varying complex Matrix coefficients. It is theoretically proved that our FTCND model can converge to the theoretical solution of time-varying linear complex Matrix Equation within finite time. In addition, the upper bound of the convergence time is derived analytically via Lyapunov theory. For comparative purposes, the conventional gradient-based neural dynamics (GND) is developed and exploited for solving such a time-varying complex problem. Computer-simulation results verify the effectiveness and superiorness of the FTCND model for solving time-varying linear complex Matrix Equation in complex domain, as compared with the GND model.
Noah H. Rhee - One of the best experts on this subject based on the ideXlab platform.
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commuting solutions of the yang baxter Matrix Equation
Applied Mathematics Letters, 2015Co-Authors: Jiu Ding, Chenhua Zhang, Noah H. RheeAbstract:Abstract Let A be a square Matrix with some special Jordan forms. When A is nonsingular, we find all the solutions of the quadratic Matrix Equation A X A = X A X , which commute with A . We also find infinitely many solutions commuting with A , depending on several parameters, when A is singular.
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further solutions of a yang baxter like Matrix Equation
East Asian Journal on Applied Mathematics, 2013Co-Authors: Jiu Ding, Chenhua Zhang, Noah H. RheeAbstract:The Yang-Baxter-like Matrix Equation AXA = XAX is reconsidered, and an infinite number of solutions that commute with any given complex square Matrix A are found. Our results here are based on the fact that the Matrix A can be replaced with its Jordan canonical form. We also discuss the explicit structure of the solutions obtained.
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spectral solutions of the yang baxter Matrix Equation
Journal of Mathematical Analysis and Applications, 2013Co-Authors: Jiu Ding, Noah H. RheeAbstract:Abstract Let A be an arbitrary square Matrix. We find a collection of solutions of the Matrix Equation of A X A = X A X in terms of the spectral projectors.
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solutions of the yang baxter Matrix Equation for an idempotent
Numerical Algebra Control and Optimization, 2013Co-Authors: A Cibotarica, Jiu Ding, J Kolibal, Noah H. RheeAbstract:Let $A$ be a square Matrix which is an idempotent. We find all solutions of the Matrix Equation of $AXA=XAX$ by using the diagonalization technique for $A$.
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A Nontrivial Solution to a Stochastic Matrix Equation
East Asian Journal on Applied Mathematics, 2012Co-Authors: Jiu Ding, Noah H. RheeAbstract:If A is a nonsingular Matrix such that its inverse is a stochastic Matrix, the classic Brouwer fixed point theorem implies that the Matrix Equation AXA = XAX has a nontrivial solution. An explicit expression of this nontrivial solution is found via the mean ergodic theorem, and fixed point iteration is considered to find a nontrivial solution.
Yunong Zhang - One of the best experts on this subject based on the ideXlab platform.
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letters zhang neural network versus gradient based neural network for time varying linear Matrix Equation solving
Neurocomputing, 2011Co-Authors: Dongsheng Guo, Yunong ZhangAbstract:A type of recurrent neural networks called Zhang neural network (ZNN) is presented and investigated to provide an online solution to the time-varying linear Matrix Equation, A(t)X(t)B(t)+X(t)=C(t) by using a novel design method. In contrast to the gradient-based neural network (GNN), the novel design of ZNN is based on a Matrix-valued indefinite error function, instead of a scalar-valued norm-based energy function. Therefore, a ZNN model depicted in implicit dynamics can globally and exponentially converge to the time-varying theoretical solution of the given linear Matrix Equation. Computer simulation results further demonstrate the superior performance of the ZNN model in solving the time-varying linear Matrix Equation compared with the conventional GNN model.
Masoud Hajarian - One of the best experts on this subject based on the ideXlab platform.
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new finite algorithm for solving the generalized nonhomogeneous yakubovich transpose Matrix Equation
Asian Journal of Control, 2017Co-Authors: Masoud HajarianAbstract:In this paper, the development of the conjugate direction CD method is constructed to solve the generalized nonhomogeneous Yakubovich-transpose Matrix Equation AXB + CXTD + EYF = R. We prove that the constructed method can obtain the least Frobenius norm solution pair X,Y of the generalized nonhomogeneous Yakubovich-transpose Matrix Equation for any special initial Matrix pair within a finite number of iterations in the absence of round-off errors. Finally, two numerical examples show that the constructed method is more efficient than other similar iterative methods in practical computation.
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efficient iterative method for solving the second order sylvester Matrix Equation evf 2 avf cv bw
Iet Control Theory and Applications, 2009Co-Authors: Mehdi Dehghan, Masoud HajarianAbstract:The second-order Sylvester Matrix Equation EVF2−AVF−CV=BW (including the generalised Sylvester Matrix Equation, normal Sylvester Matrix Equation and Lyapunov Matrix Equation as special cases) over unknown Matrix pair [V, W], has wide applications in many fields. In the present study, the authors propose an iterative method to solve the second-order Sylvester Matrix Equation. The proposed iterative method does not depend on the Jordan form of the Matrix F. By this iterative method, the solvability of the Matrix Equation can be determined automatically over unknown Matrix pair [V, W]≠0. When the Matrix Equation is solvable, its solution pair can be obtained within finite iterative steps, and its least Frobenius norm solution pair can be obtained by choosing suitable initial Matrix pair. Furthermore, its optimal approximation solution pair to a given Matrix pair can be derived by finding the least norm solution pair of a new Matrix Equation. A numerical example is given to show the efficiency of the proposed method.
Mehdi Dehghan - One of the best experts on this subject based on the ideXlab platform.
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hss like method for solving complex nonlinear yang baxter Matrix Equation
Engineering With Computers, 2020Co-Authors: Mehdi Dehghan, Akbar ShirilordAbstract:Many works on solving Matrix Equations are related to the complex nonlinear Yang–Baxter Matrix Equation $$ AXA=XAX $$, where $$ A \in {\mathbb {C}}^{n \times n}$$ is a given Matrix and X is an unknown Matrix. The Yang–Baxter Matrix Equation has been widely studied by its application in various fields of mathematics and physics. In this paper, we introduce an iterative method based on the Hermitian and skew-Hermitian splitting of coefficient Matrix A for solving complex nonlinear Yang–Baxter Matrix Equation. Then, we prove the convergence of the new scheme subject to some conditions. Finally, an example is solved to discover the applicability of the new method via comparing it with some related previous methods.
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efficient iterative method for solving the second order sylvester Matrix Equation evf 2 avf cv bw
Iet Control Theory and Applications, 2009Co-Authors: Mehdi Dehghan, Masoud HajarianAbstract:The second-order Sylvester Matrix Equation EVF2−AVF−CV=BW (including the generalised Sylvester Matrix Equation, normal Sylvester Matrix Equation and Lyapunov Matrix Equation as special cases) over unknown Matrix pair [V, W], has wide applications in many fields. In the present study, the authors propose an iterative method to solve the second-order Sylvester Matrix Equation. The proposed iterative method does not depend on the Jordan form of the Matrix F. By this iterative method, the solvability of the Matrix Equation can be determined automatically over unknown Matrix pair [V, W]≠0. When the Matrix Equation is solvable, its solution pair can be obtained within finite iterative steps, and its least Frobenius norm solution pair can be obtained by choosing suitable initial Matrix pair. Furthermore, its optimal approximation solution pair to a given Matrix pair can be derived by finding the least norm solution pair of a new Matrix Equation. A numerical example is given to show the efficiency of the proposed method.
