A relaxed gradient based algorithm for solving sylvester equations

Niu, Qiang; Wang, Xiang; Lu, Linzhang

doi:10.1002/asjc.328

Cited by 82 publications

(67 citation statements)

References 9 publications

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“…Numerical results illustrate that the proposed method is correct and feasible. We must point out that the ideas in this paper have some differences comparing with that in [28,[34][35][36].…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 91%

“…The convergence properties of the methods are investigated in [27,32]. Niu et al [34] proposed a relaxed gradient based iterative algorithm for solving Sylvester equations. Wang et al [35] proposed a modified gradient based iterative algorithm for solving Sylvester equations (1).…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…In this paper, inspired by [28,[34][35][36], we first derive a relaxed gradient based iterative (RGI) algorithm for solving the symmetric solution of matrix equation (1). Theoretical analysis shows that our method converges to the exact symmetric solution for any initial value with some appropriate assumptions.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

See 2 more Smart Citations

The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation AX + XB = C

Zhang

Sheng

2017

Mathematical Problems in Engineering

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In this paper, we present two different relaxed gradient based iterative (RGI) algorithms for solving the symmetric and skew symmetric solution of the Sylvester matrix equation + = . By using these two iterative methods, it is proved that the iterative solution converges to its true symmetric (skew symmetric) solution under some appropriate assumptions when any initial symmetric (skew symmetric) matrix 0 is taken. Finally, two numerical examples are given to illustrate that the introduced iterative algorithms are more efficient.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 91%

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

See 1 more Smart Citation

The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation AX + XB = C

Zhang

Sheng

2017

Mathematical Problems in Engineering

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“…Therefore, the problem has remained an active area of research. In this context, recent methodological advances have been thoroughly discussed in many papers [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Iterative methods for solving linear or nonlinear equations have seen constant improvement in recent years to reduce the computational time; for example, two multi-step derivative-free iterative methods [5]: block Jacobi two stage method [6] and SYMMLQ algorithm [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

“…However, this method is not applicable in large-scale problems due to the prohibitive computational issue. In order to overcome this limitation, fast iterative methods have been developed such as the Smith method [12], the alternating direction implicit (ADI) method [13], gradient-based methods [14,15], and the Krylov subspace-based algorithm [7,16,17]. At present, the conjugate gradient (CG) method [7] and the preconditioned conjugate gradient method [18] are popularly used with the advantages of small storage and suitability for parallel computing.…”

Section: Introductionmentioning

confidence: 99%

A Parallel Two-Stage Iteration Method for Solving Continuous Sylvester Equations

et al. 2017

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Abstract:In this paper we propose a parallel two-stage iteration algorithm for solving large-scale continuous Sylvester equations. By splitting the coefficient matrices, the original linear system is transformed into a symmetric linear system which is then solved by using the SYMMLQ algorithm. In order to improve the relative parallel efficiency, an adjusting strategy is explored during the iteration calculation of the SYMMLQ algorithm to decrease the degree of the reduce-operator from two to one communications at each step. Moreover, the convergence of the iteration scheme is discussed, and finally numerical results are reported showing that the proposed method is an efficient and robust algorithm for this class of continuous Sylvester equations on a parallel machine.

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

Ramadan

Bayoumi

2017

Asian Journal of Control

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In this paper, we present a modified gradient-based algorithm for solving extended Sylvester-conjugate matrix equations. The idea is from the gradient-based method introduced in [14] and the relaxed gradient-based algorithm proposed in [16]. The convergence analysis of the algorithm is investigated. We show that the iterative solution converges to the exact solution for any initial value based on some appropriate assumptions. A numerical example is given to illustrate the effectiveness of the proposed method and to test its efficiency and accuracy compared with those presented in [14] and [16].

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A relaxed gradient based algorithm for solving sylvester equations

Cited by 82 publications

References 9 publications

The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation AX + XB = C

The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation AX + XB = C

A Parallel Two-Stage Iteration Method for Solving Continuous Sylvester Equations

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

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