Extremal signatures for bivariate Chebyshev approximation problems

The problem of finding a Chebyshev solution of the real matrix equationAX+YB=C, whereC is anm×n matrix, is considered. This equation is equivalent to a linear system [I_nA,B^TI_m]z=d. The characterization and the computation of best linear Chebyshev approximations are connected with the notion of extremal signature. The purpose of this paper is to analyze the extremal signatures of this problem.