Constraints definition and evaluation of piecewise polynomial approximation functions for embedded systems

A procedure for defining the constraints and limits for approximating a non-linear function by piecewise polynomial functions is presented. We consider the free variable to be generated with an associated uncertainty. Also, the calculation is carried out using fixed-point arithmetic with limited resolution, which is more suitable for implementing in embedded systems with low computational power. An evaluation test for approximated function solutions, which can be used for comparing several solutions yielded by different procedures, is also proposed. An example of a non-linear function approximation is presented in order to illustrate the proposed procedures.