Solution of the matrix equation AX? XB = C

Shestopal, V. E.

doi:10.1007/bf01437863

Cited by 4 publications

(4 citation statements)

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“…Numerical algorithms for solving the Sylvester equation were studied in [2]. Actually, the two earliest methods are the Bartels-Stewart algorithm [3] and the Hessenberg-Schur method [4]. Both methods convert original equation to attractable form by a Schur decomposition.…”

Section: Introductionmentioning

confidence: 99%

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An efficient method for solving non-negative Sylvester matrix equations

Zhou

2023

Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022)

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Alternating Direction Method of Multipliers (ADMM) is an effective method for solving separable convex optimization problems. In this paper, the method is extended to solve Sylvester equations with nonnegative constraint. We give a convergence result showing that the algorithm converges to a Karush-Kuhn-Tucker point whenever it converges. Numerical evidence shows that the proposed algorithm can efficiently solve nonnegative Sylvester equations.

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Section: Introductionmentioning

confidence: 99%

“…Both methods convert original equation to attractable form by a Schur decomposition. Bartels-Stewart algorithm in [3] transformed A and B into real Schur forms. In [4], the matrix A is converted to upper Hessenberg and the matrix B is transformed into real Schur form.…”

Section: Introductionmentioning

confidence: 99%

An efficient method for solving non-negative Sylvester matrix equations

Zhou

2023

Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022)

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“…According to [15], the solution of this equation has the following form [ If B A = -T in (2.1), then Eq. (2.1) will go over into the Lyapunov equation (1.1).…”

Section: Introductionmentioning

confidence: 99%

“…(1.1) represented by (2.2) is asymmetric. Expression (2.2) follows from a more general expression derived in [15]. Namely, if Formula (2.2) can be obtained if P( ) t in (2.6) is set equal to P t A ( ).…”

Section: Introductionmentioning

confidence: 99%

Solutions of matrix equations in problems of mechanics and control

Larin

2009

Int Appl Mech

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The paper considers algorithms for solving linear matrix equations related to problems of mechanics and control, namely, the Lyapunov and Sylvester matrix equations and Riccati-type nonlinear matrix equations. These algorithms are capable of solving both linear equations and linear matrix inequalities. Algorithms based on the Bass relations are used to solve Riccati-type nonlinear matrix equations in so-called special cases where some eigenvalues of the matrix pencil are on a unit circle. These algorithms are compared with those of other authors by way of examples. It is shown that the algorithms can be implemented in symbolic computing routings, which allows solving these equations with high accuracy

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