On 2D Inverse Problems/The inverse problems

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:

The weights of the paths are elementary symmetric functions of the weights of individual edges

(Hint). The boundary data consists of values of the elementary symmetric functions of the weights a,b,c,d.