Gradient based iterative algorithms for solving a class of matrix equations

By Feng Ding, Tongwen Chen. IEEE Transactions on Automatic Control, 2005

503 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/402b37c1d84068a520f7f301ffb6ecea526c1c5d

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Citations in the corpus

On the generalized bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations (2011, methodology): “By expanding the matrix equation in [11], we obtain the system of generalized Sylvester matrix equations Xl i1⁄41 AiYBi 1⁄4M, Xl i1⁄41 CiYDi 1⁄4 N, ð1:1Þ”
Weighted least squares solutions to general coupled Sylvester matrix equations (2009, methodology): “By using the hierarchical identification principle, iterative algorithms are proposed in [21–24] to solve general linear matrix equations and coupled Sylvester matrix equations.”
Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle (2008, methodology): “Consider a linear system described by a set of equation [1] [2] [3] [4] [5], Ax ¼ b; A 2 R mÂn ; b 2 R m : ð1Þ Here, x 2 R n is an unknown vector to be solved.”
The generalized centro‐symmetric and least squares generalized centro‐symmetric solutions of the matrix equation AYB + CYTD = E (2011, methodology): “Ding and Chen introduced the hierarchical least squares-iterative (HLSI) algorithms for several coupled matrix equations [32, 33] and the hierarchical gradient-iterative (HGI) algorithms for general matrix equations [34, 35].”
On Iterative Solutions of General Coupled Matrix Equations (2006, methodology): “Also, if parameters in system matrices contain uncertainty, it is not possible to obtain exact solutions for robust stability analysis [9, 10, 13, 24, 23, 21].”
Accelerating a Recurrent Neural Network to Finite-Time Convergence for Solving Time-Varying Sylvester Equation by Using a Sign-Bi-power Activation Function (2012, methodology): “Various gradient-based recurrent neural networks particularly designed for solving Sylvester equation are proposed [16–19].”
The general solutions to some systems of matrix equations (2015, unknown): “[1–46]).”
A relaxed gradient based algorithm for solving sylvester equations (2011, methodology): “We should point out that formula (12) reduces to the one used in [7] if =0.”
A GRADIENT BASED ADAPTIVE CONTROL ALGORITHM FOR DUAL‐RATE SYSTEMS (2006, background): “Notice that the number of model parameters will be increased after the polynomial transform; this will lead to increased computational complexity, which may be reduced by using the hierarchical identification scheme [13,24-27].”
The general coupled matrix equations over generalized bisymmetric matrices (2010, methodology): “The gradient-based iterative (GI) algorithms [15,20] and least squares based iterative algorithm [16] for solving (coupled) matrix equations are innovational and computationally efficient numerical algorithms and were presented based on the hierarchical identification principle [17,18] which regards”