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**Gradient based iterative solutions for general linear matrix equations.**
*(English)*
Zbl 1189.65083

Summary: We present a gradient based iterative algorithm for solving general linear matrix equations by extending the Jacobi iteration and by applying the hierarchical identification principle. Convergence analysis indicates that the iterative solutions always converge fast to the exact solutions for any initial values and small condition numbers of the associated matrices. Two numerical examples are provided to show that the proposed algorithm is effective.

### MSC:

65F30 | Other matrix algorithms (MSC2010) |

15A24 | Matrix equations and identities |

### Keywords:

Lyapunov matrix equations; Sylvester matrix equations; iterations; least-squares; estimation
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\textit{L. Xie} et al., Comput. Math. Appl. 58, No. 7, 1441--1448 (2009; Zbl 1189.65083)

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### References:

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