NONNEGATIVE SOLUTIONS AND POSITIVE RESOLVING KERNELS WITH NEGATIVE SOLUTION AVERAGES IN LINEAR INVERSE-THEORY

Using the duality theorem of linear programming, it is shown that, for a linear inverse problem, the non-existence of a non-negative solutio n is equivalent to the existence of a positive-resolving kernel associ ated with a negative solution average. If no such resolving kernel can be found, we are then guaranteed the existence of a non-negative solu tion.