  The analysis of complex nonlinear systems is often carried out using simpler
piecewise linear representations of them. A principled and practical technique
is proposed to linearize and evaluate arbitrary continuous nonlinear functions
using polygonal (continuous piecewise linear) models under the L1 norm. A
thorough error analysis is developed to guide an optimal design of two kinds of
polygonal approximations in the asymptotic case of a large budget of evaluation
subintervals N. The method allows the user to obtain the level of linearization
(N) for a target approximation error and vice versa. It is suitable for, but
not limited to, an efficient implementation in modern Graphics Processing Units
(GPUs), allowing real-time performance of computationally demanding
applications. The quality and efficiency of the technique has been measured in
detail on two nonlinear functions that are widely used in many areas of
scientific computing and are expensive to evaluate
