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Nonlinearity recovery by standard and aggregative orthogonal series algorithms
Author(s) -
Śliwiński Przemysław,
Wachel Paweł,
Łagosz Szymon
Publication year - 2018
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2311
Subject(s) - series (stratigraphy) , smoothness , algorithm , nonlinear system , regular polygon , computer science , mathematics , mathematical optimization , nonlinear programming , mathematical analysis , paleontology , physics , geometry , quantum mechanics , biology
In this paper, the problem of nonlinearity recovery in Hammerstein systems is considered. Two algorithms are presented: the first is a standard orthogonal series algorithm, whereas the other, ie, the aggregative one, exploits the convex programming approach. The finite sample size properties of both approaches are examined, compared, and illustrated in a numerical experiment. The aggregative algorithm performs better when the number of measurements is comparable to the number of parameters; however, it also imposes additional smoothness restrictions on the recovered nonlinearities.