Technical Note - Inversion of systems of quadratic equations

Abstract

Inversion of linear systems of equations is straightforward, although there are some complications when the equations represent a physical process and there is noise in the measurements of the dependent variables. This paper extends the linear inversion method to systems of quadratic equations. Using this method, we can devise better inversion algorithms, and better estimates of the error in the inversion process, by including quadratic terms explicitly. Two different ways that quadratic terms can be included are suggested. The method used will depend largely on the relative sizes of the various non-linear terms. This method will also greatly improve our ability to evaluate the potential performance of proposed sensor systems. I believe that this is a new approach to this problem.