Properties of the ℓ1-solutions of the Linear Matrix Equation AX+YB=C
Krystyna Ziętak · IMA Journal of Numerical Analysis · 1987
The properties of the ℓ1 of the linear matrix equation AX+YB=C are investigated, where A, B, and C are given real matrices of dimensions m × r, s × n, and m × n, respectively, with m > r and n > s. An algorithm which is an ℓ1version of the general alternating method is developed. This algorithm utilizes a special form of the equation AX+YB=C and adjusts X and Y alternately. It gives an ℓ1-solution of AX+YB=C under additional assumptions. Some numerical examples are given.