Abstract
Conditions for the unique solvability of matrix equations of the form AX + BX T = X and AX + BX* = C are found. Numerical algorithms of the Bartels-Stewart type for solving such equations are described. Certain numerical tests with these algorithms are presented. In particular, the situation where the conditions for unique solvability are “almost” violated is modeled, and the deterioration of the quality of the computed solution in this situation is traced through.
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