## Least squares solution with the minimum-norm to general matrix equations via iteration.(English)Zbl 1186.65047

Two 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.

### MSC:

 65F20 Numerical solutions to overdetermined systems, pseudoinverses 65F30 Other matrix algorithms (MSC2010) 15A24 Matrix equations and identities
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### References:

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