Iterative least-squares solutions of coupled Sylvester matrix equations

By Feng Ding, Tongwen Chen. Systems & control letters (Print), 2005

452 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/0e4e9002fe1c58bb178a68291ddc8b9888ce90e5

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In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

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].”
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].”
Hierarchical least squares identification methods for multivariable systems (2005, unknown): “REFERENCES [1] A. Rachid, " Robustness of discrete systems under structured uncertainties , " Int.”
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.”
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 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”
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”
Computational Methods for Linear Matrix Equations (2016, methodology): “A similar framework is used in [74] where more than two unknown matrices are allowed, and an approximate solution is obtained by means of a least squares approach.”
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”