A modified gradient‐based algorithm for solving extended Sylvester‐conjugate matrix equations

Ramadan, Mohamed A.; Bayoumi, Ahmed M. E.

doi:10.1002/asjc.1574

Cited by 18 publications

(10 citation statements)

References 19 publications

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“…In this section, we will give two numerical examples to illustrate the efficiency of Algorithm 1. In order to illustrate the computational effectiveness of Algorithm 1, we compare Algorithm 1 with GI and CGNE algorithms (Beik et al, 2014; Dehghan and Hajarian, 2012; Hajarian, 2018; Ramadan and Bayoumi, 2018; Zhang, 2017). All the tests are performed by MATLAB 7.0 with machine precision around 10 − 16 .…”

Section: Numerical Examplesmentioning

confidence: 99%

Iterative method to the coupled operator matrix equations with sub-matrix constraint and its application in control

Song

2020

Transactions of the Institute of Measurement and Control

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A finite iterative algorithm is presented for solving the numerical solutions to the coupled operator matrix equations in Zhang (2017b). In this paper, a new finite iterative algorithm is presented for solving the constraint solutions to the coupled operator matrix equations [Formula: see text], where the constraint solutions include symmetric solutions, bisymmetric solutions and reflexive solutions as special cases. If this system is consistent, for any initial constraint matrices, the exact constraint solutions can be obtained by the introduced algorithm within finite iterative steps in the absence of the roundoff errors. Also, if this system is not consistent, the least-norm constraint solutions can be obtained within the finite iteration steps in the absence of the roundoff errors. Furthermore, if a group of suitable matrices are given, the optimal approximation solutions can be derived. Finally, several numerical examples are given to show the effectiveness of the presented iterative algorithm.

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Section: Numerical Examplesmentioning

confidence: 99%

Iterative method to the coupled operator matrix equations with sub-matrix constraint and its application in control

Song

2020

Transactions of the Institute of Measurement and Control

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“…Here, we generalize the conjugate gradient normal equation residual (CGNR) method and the conjugate gradient normal equation error (CGNE) method for solving Problem 2. In recent years, Ramadan and Bayoumi (2018); Xie et al (2014); and Dehghan and Hajarian (2011, 2010a,b) extended the CGNR and CGNE methods to solve several Sylvester matrix equations. As is well known, the CGNR and CGNE methods are obtained by applying the CG algorithm for solving either linear systems…”

Section: Algorithm and Its Convergence Analysismentioning

confidence: 99%

Partially doubly symmetric solutions of general Sylvester matrix equations

Hajarian

2019

Transactions of the Institute of Measurement and Control

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The study of linear matrix equations is extremely important in many scientific fields such as control systems and stability analysis. In this work, we aim to design the Hestenes-Stiefel (HS) version of biconjugate residual (Bi-CR) algorithm for computing the (least Frobenius norm) partially doubly symmetric solution [Formula: see text] of the general Sylvester matrix equations [Formula: see text] for [Formula: see text]. We show that the proposed algorithm converges in a finite number of iterations. Finally, numerical results compare the proposed algorithm to alternative algorithms.

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“…and a finite iterative algorithm for solving a complex of conjugate and transpose matrix equation Ramadan and Bayoumi (2018) presented a modified gradient-based algorithm for solving extended Sylvesterconjugate matrix equation ( 1). An accelerated gradient-based iterative algorithm for solving extended Sylvester-conjugate matrix equation (1) has been presented by Bayoumi and Ramadan (2018).…”

Section: Introductionmentioning

confidence: 99%

A relaxed gradient based iterative algorithm of the generalized Sylvester-conjugate matrix equation over centro-symmetric and centro-Hermitian matrices

El-Shazly

Ramadan

El-Sharway

2022

Journal of Vibration and Control

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The main purpose of this paper is to establish two relaxed gradient-based iterative (RGI) algorithms extending the Jacobi and Gauss–Seidel iterations for solving the generalized Sylvester-conjugate matrix equation [Formula: see text], over centro-symmetric, and centro-Hermitian matrices. It is shown that the iterative methods, respectively, converge to the centro-symmetric and centro-Hermitian solutions for any initial centro-symmetric and centro-Hermitian matrices. We report numerical tests to show the effectiveness of the proposed approaches.

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A modified gradient‐based algorithm for solving extended Sylvester‐conjugate matrix equations

Cited by 18 publications

References 19 publications

Iterative method to the coupled operator matrix equations with sub-matrix constraint and its application in control

Iterative method to the coupled operator matrix equations with sub-matrix constraint and its application in control

Partially doubly symmetric solutions of general Sylvester matrix equations

A relaxed gradient based iterative algorithm of the generalized Sylvester-conjugate matrix equation over centro-symmetric and centro-Hermitian matrices

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