On Iterative Solutions of General Coupled Matrix Equations

By Feng Ding, Tongwen Chen. SIAM Journal of Control and Optimization, 2006

390 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/3870c7fe19faca53e166691b68039f6220717d5a

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Numerical Analysis

Citations in the corpus

The general coupled matrix equations over generalized bisymmetric matrices (2010, methodology): “Also Ding and Chen [19], applying the gradient search principle and the hierarchical identification principle, presented the gradient-based iterative algorithms for the general coupled 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.”
A relaxed gradient based algorithm for solving sylvester equations (2011, methodology): “Chen propose some interesting and computationally efficient gradient-based [6, 7] and least squares based [8] iterative methods for solving general matrix equations.”
On the generalized reflexive and anti-reflexive solutions to a system of matrix equations (2012, methodology): “The HGI algorithms [16,21] and HLSI algorithms [20,21,18] for solving general (coupled) matrix equations are innovational and computationally efficient numerical methods and were proposed based on the hierarchical identification principle [17,19] which regards the unknown matrix as the system parame”
The generalized centro‐symmetric and least squares generalized centro‐symmetric solutions of the matrix equation AYB + CYTD = E (2011, methodology): “The HGI algorithms [34, 35] and HLSI algorithms [33, 35, 36] for solving general (coupled) matrix equations are innovational and computationally efficient numerical methods and were proposed based on the hierarchical identification principle [32, 37] which regards the unknown matrix as the system pa”
On the generalized bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations (2011, methodology): “The HGI algorithms [11,16] and HLSI algorithms [13,15,16] for solving general (coupled) matrix equations are innovative and computationally efficient numerical algorithms and were proposed based on the hierarchical identification principle [12,14] which regards the unknown matrix as the system param”
Weighted least squares solutions to general coupled Sylvester matrix equations (2009, methodology): “We note that if p = q, iterative algorithms are proposed in [21,24], to solve Problem 3 by using the hierarchical identification principle.”