On the Unique Solvability of the Generalized Absolute Value Matrix Equation

The generalized absolute value matrix equation has application in a variety of optimization problems, its unique solvability is still on the way. In this note, the unique solvability of the generalized absolute value matrix equation is considered. A new unique solvability of generalized absolute value matrix equation is given. The obtained result can be regarded as an extension of the absolute value equation to the generalized absolute value matrix equation. As an application, new convergence of matrix multisplitting Picard-iterative method is presented.