high performance computing on graphics processing units: hgpu.org

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. We propose a principled and practical technique 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 the Gaussian function because it is a nonlinear function extensively used in many areas of scientific computing and it is expensive to evaluate.