A relaxed gradient based algorithm for solving Sylvester equations. (English) Zbl 1242.65081

A new iterative method for the numerical solution of the Sylvester matrix equation \(AX + YB = C\) is proposed. By the introduction of a relaxation parameter, a relaxed gradient based iterative algorithm for solving the Sylvester equation is developed. A theoretical analysis shows that the new method converges under certain assumptions. Comparisons are performed with the original algorithm, and results show that the new method exhibits a fast convergence behavior with a wide range of relaxation parameters.


65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities
65F10 Iterative numerical methods for linear systems
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