Least squares solution with the minimum-norm to general matrix equations via iteration.

*(English)*Zbl 1186.65047Two iterative algorithm are presented to solve the minimal norm least squares solution to a general linear matrix equations including the well-known Sylvester matrix equation and Lyapunov matrix equation as special cases. The first algorithm is based on the gradient based searching principle and the other one can be viewed as its dual. Necessary and sufficient conditions for the step sizes in these two algorithms are proposed to guarantee the convergence of the algorithms for arbitrary initial conditions.

Reviewer: Rózsa Horvàth-Bokor (Budapest)

##### MSC:

65F20 | Numerical solutions to overdetermined systems, pseudoinverses |

65F30 | Other matrix algorithms (MSC2010) |

15A24 | Matrix equations and identities |

##### Keywords:

iterative algorithm; minimal norm least squares solution; optimal step size; convergence; general linear matrix equations; Sylvester matrix equation; Lyapunov matrix equation
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\textit{Z.-Y. Li} et al., Appl. Math. Comput. 215, No. 10, 3547--3562 (2010; Zbl 1186.65047)

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