Dykstra’s
alternating projection algorithm was proposed to treat the problem of finding
the projection of a given point onto the intersection of some closed convex
sets. In this paper, we first apply Dykstra’s alternating projection algorithm
to compute the optimal approximate symmetric positive semidefinite solution of
the matrix equations AXB = E, CXD = F. If we choose the initial
iterative matrix X0 = 0,
the least Frobenius norm symmetric positive semidefinite solution of these
matrix equations is obtained. A numerical example shows that the new algorithm
is feasible and effective.
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