Optimal polygonal L1 linearization and fast interpolation of nonlinear systems

Gallego Bonet, Guillermo and Berjón Díez, Daniel and García Santos, Narciso (2014). Optimal polygonal L1 linearization and fast interpolation of nonlinear systems. "IEEE Transactions on Circuits and Systems I: Regular Papers", v. 61 (n. 11); pp. 3225-3234. ISSN 1549-8328. https://doi.org/10.1109/TCSI.2014.2327313.

Description

Title: Optimal polygonal L1 linearization and fast interpolation of nonlinear systems
Author/s:
  • Gallego Bonet, Guillermo
  • Berjón Díez, Daniel
  • García Santos, Narciso
Item Type: Article
Título de Revista/Publicación: IEEE Transactions on Circuits and Systems I: Regular Papers
Date: November 2014
ISSN: 1549-8328
Volume: 61
Subjects:
Freetext Keywords: Piecewise linearization, numerical approximation and analysis, least-first-power, optimization, function approximation, error analysis.
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Señales, Sistemas y Radiocomunicaciones
UPM's Research Group: Tratamiento de Imágenes GTI
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

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.

More information

Item ID: 25643
DC Identifier: http://oa.upm.es/25643/
OAI Identifier: oai:oa.upm.es:25643
DOI: 10.1109/TCSI.2014.2327313
Deposited by: Dr Guillermo Gallego Bonet
Deposited on: 29 Apr 2014 06:31
Last Modified: 29 May 2015 10:52
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