Boundary Value Problems on Finite Networks

Abstract

This chapter is motivated by a well-known matrix problem; specifically, the M- matrix inverse problem, as we will see in the next section. Our approach differs from others because the tools we use come from discrete potential theory, in which we have been working for a long period, trying to emulate as much as possible the continuous case. This chapter introduces this way of approximating a problem typical of matrix theory and offers an overview of the potential power of introducing new approaches in this field.