A merging formula describes how to compute the scattering matrix of an object from the scattering matrices of its non-overlapping
pieces. Splitting is when the merging formula is solved as an equation
for the scattering matrices of the pieces. We will describe how the
ill-posed, nonlinear, inverse problem can be split into a problem that
is nonlinear but well-posed, and a problem that is ill-posed but linear. Moreover, we will show that there is an explicit formula for the solution of the well-posed, nonlinear problem.
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