Two iterative algorithms for solving coupled matrix equations over reflexive and anti-reflexive matrices

Dehghan, Mehdi; Hajarian, Masoud

doi:10.1590/s1807-03022012000200008

Cited by 14 publications

(6 citation statements)

References 42 publications

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“…Several iterative methods have been proposed for solving linear matrix equations in the literature; for instance see [3,4,[9][10][11][12][13][14][15] and the references therein. The earlier cited works have been mainly proposed the GB approaches to solve different kinds of matrix equations under the restrictions that the problem has a unique solution.…”

Section: An Algorithm With Dors For Matrix Equationsmentioning

confidence: 99%

Delayed over-relaxation in iterative schemes to solve rank deficient linear system of (matrix) equations

Ameri¹,

Panjeh²

2018

Filomat

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Recently in [Journal of Computational Physics, 321 (2016), 829-907], an approach has been developed for solving linear system of equations with nonsingular coefficient matrix. The method is derived by using a delayed over-relaxation step (DORS) in a generic (convergent) basic stationary iterative method. In this paper, we first prove semi-convergence of iterative methods with DORS to solve singular linear system of equations. In particular, we propose applying the DORS in the Modified HSS (MHSS) to solve singular complex symmetric systems and in the Richardson method to solve normal equations. Moreover, based on the obtained results, an algorithm is developed for solving coupled matrix equations. It is seen that the proposed method outperforms the relaxed gradient-based (RGB) method [Comput. Math. Appl. 74 (2017), no. 3, 597-604] for solving coupled matrix equations. Numerical results are examined to illustrate the validity of the established results and applicability of the presented algorithms.

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Section: An Algorithm With Dors For Matrix Equationsmentioning

confidence: 99%

Delayed over-relaxation in iterative schemes to solve rank deficient linear system of (matrix) equations

Ameri¹,

Panjeh²

2018

Filomat

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“…Algebraic Sylvester matrix equations are observed in many areas from different regions such as, control theory and many other branches of engineering [7][8][9]23].…”

Section: Introductionmentioning

confidence: 99%

On the CRI method for solving Sylvester equation with complex symmetric positive semi-definite coefficient matrices

Karamali

Shirilord

Dehghan

2021

Filomat

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Combination of real and imaginary parts (CRI) method is an efficient method for solving a class of large sparse linear systems with complex symmetric positive semi-definite coefficient matrices. In this work we will extend CRI approach to determine the approximate solution of Sylvester equation with complex symmetric semi-definite positive coefficient matrices. We show that the new algorithm converges unconditionally to the unique exact solution of the Sylvester matrix equation. In the end we test the new scheme by solving some numerical examples.

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“…For example, Wang et al derived the hierarchical least squares based iterative algorithm for the Box-Jenkins system [15]; and Dehghan and Hajarian presented the iterative method for solving systems of linear matrix equations over reflexive and anti-reflexive matrices [16]. Compared with the recursive identification algorithm, the iterative identification algorithm uses all the measured data to refresh parameter estimation, so the parameter estimation accuracy can be greatly improved, and the iterative identification methods have been successfully applied to many different models [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Data Filtering Based Recursive and Iterative Least Squares Algorithms for Parameter Estimation of Multi-Input Output Systems

Ding

2016

Algorithms

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This paper discusses the parameter estimation problems of multi-input output-error autoregressive (OEAR) systems. By combining the auxiliary model identification idea and the data filtering technique, a data filtering based recursive generalized least squares (F-RGLS) identification algorithm and a data filtering based iterative least squares (F-LSI) identification algorithm are derived. Compared with the F-RGLS algorithm, the proposed F-LSI algorithm is more effective and can generate more accurate parameter estimates. The simulation results confirm this conclusion.

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Two iterative algorithms for solving coupled matrix equations over reflexive and anti-reflexive matrices

Cited by 14 publications

References 42 publications

Delayed over-relaxation in iterative schemes to solve rank deficient linear system of (matrix) equations

Delayed over-relaxation in iterative schemes to solve rank deficient linear system of (matrix) equations

On the CRI method for solving Sylvester equation with complex symmetric positive semi-definite coefficient matrices

Data Filtering Based Recursive and Iterative Least Squares Algorithms for Parameter Estimation of Multi-Input Output Systems

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