Weighted integral method for algebraic inversion: Theoretical consideration with a toy problem

The weighted integral (of differential) method is a general mathematical framework proposed recently for estimating parameters of physical/signal field including sources [1], [2], [3], [4], [5], [6], [7], [8]. It provides exact algebraic relations for solving their parameters from finite-supported observations. To establish it more practically and mathematically, several issues must be further considered. In this paper, we give some consideration on this method and comparison with other least-squares methods using a very simple problem as an example.