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An iterative method for the skew-symmetric solution and the optimal approximate solution of the matrix equation $AXB=C$. (English) Zbl 1146.65036
The authors introduce a simple algorithm to decide whether the matrix equation $AXB=C$ with compatibly dimensioned given matrices $A,B$, and $C$ has a skew-symmetric solution $X$. The algorithm finds this solution – if possible – in finitely many iterations for any given error bound. Moreover the same matrix equation for a modified right hand side $\stackrel{˜}{C}$ and $\stackrel{˜}{X}$ can be used to find the minimal norm skew-symmetric solution $X$ to the original $AXB=C$ equation. Both algorithms work for any skew-symmetric starting matrix.

##### MSC:
 65F30 Other matrix algorithms 15A24 Matrix equations and identities
##### Keywords:
matrix equation; skew-symmetric solution; iterative method
##### References:
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