11174

Optimal polygonal L1 linearization and fast interpolation of nonlinear systems

Guillermo Gallego, Daniel Berjon, Narciso Garcia
Grupo de Tratamiento de Imagenes (GTI), ETSI Telecomunicacion, Universidad Politecnica de Madrid, Madrid, Spain
arXiv:1312.7815 [math.OC], (30 Dec 2013)

@article{2013arXiv1312.7815G,

   author={Gallego}, G. and {Berj{‘o}n}, D. and {Garc{‘{i}}a}, N.},

   title={"{Optimal polygonal L1 linearization and fast interpolation of nonlinear systems}"},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1312.7815},

   primaryClass={"math.OC"},

   keywords={Mathematics – Optimization and Control, Computer Science – Systems and Control, Mathematics – Numerical Analysis},

   year={2013},

   month={dec},

   adsurl={http://adsabs.harvard.edu/abs/2013arXiv1312.7815G},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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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.
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