The problem of approximating ann x m matrixC by matrices of the formX A+B Y whereA, B, X andY are of appropriate size is considered. The measure of error is the supremum of the absolute values of the individual entries in the error matrix. The problem is closely related to that of approximating a bivariate functionf by sums of functions of the formxh+gy wherex andg are functions of the first variable alone andh andy are functions of the second variable. An old algorithm for constructing best approximations is described, and some of the properties of its convergence are discussed.