The inverse problems, that we discuss in this book are the problems of inferring the local and global properties of networks or manifolds from the solutions of difference/differential equations defined on the domains (the measurement data). There're two types of the problems: inverse boundary problems (the boundary values of the solutions) and inverse spectral problems (the spectral data of difference or differential operators). This book considers both and also the relationship b/w the continuous/discrete inverse problems on the manifolds/embedded networks.
Exercise (*). Restate the problem of finding roots of a polynomial as an inverse problem for the weighted directed graph of the following type:
(Hint). The boundary data consists of values of the elementary symmetric functions of the weights a,b,c,d.