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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 876862, 9 pages
http://dx.doi.org/10.1155/2015/876862
Research Article

Models and Algorithms for Optimal Piecewise-Linear Function Approximation

1Department of Automation and Systems Engineering, Federal University of Santa Catarina, Cx.P. 476, 88040-900 Florianópolis, SC, Brazil
2Instituto Federal Catarinense, Estrada do Redentor, No. 5665, 89163-356 Rio do Sul, SC, Brazil

Received 4 March 2015; Accepted 11 June 2015

Academic Editor: Jean-Christophe Ponsart

Copyright © 2015 Eduardo Camponogara and Luiz Fernando Nazari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Piecewise-linear functions can approximate nonlinear and unknown functions for which only sample points are available. This paper presents a range of piecewise-linear models and algorithms to aid engineers to find an approximation that fits best their applications. The models include piecewise-linear functions with a fixed and maximum number of linear segments, lower and upper envelopes, strategies to ensure continuity, and a generalization of these models for stochastic functions whose data points are random variables. Derived from recursive formulations, the algorithms are applied to the approximation of the production function of gas-lifted oil wells.