Numerical solution of a class of quasi-linear matrix equations

Given the matrix equation AX+XB+f(X)C=D in the unknown n×m matrix X, we analyze existence and uniqueness conditions, together with computational solution strategies for f:Rn×m→R being a linear or nonlinear function. We characterize different properties of the matrix equation and of its solution, depending on the considered classes of functions f. Our analysis mainly concerns small dimensional problems, though several considerations also apply to large scale matrix equations.