Linearality of polynomial models of discrete time series

Aihua Li, Serpil Saydam

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Consider a time series T and the set of polynomial models of T. We discuss two types of linearalities of T. The first type is measured by the maximal number of linear members of a polynomial model may have, denoted LN(T). An upper bound for LN(T) is given. The other is measured by the number of linear elements in a Gröbner Basis G of the ideal vanishing at all points of T, denoted LIN(G). Note that for each selected term order on the monomials of F[x1, ..., xn], there is a unique generating set, called the reduced Gröbner Basis, for the vanishing ideal mentioned above. We give a method to find linear members in G with respect to any term order. When selecting a graded term order (total degree prefered), we give a formula for the cardinality of LIN(G). Sample models are illustrated to support the theorems and propositions and they are constructed using the Buchberger Möller Algorithm.

Original languageEnglish
Title of host publicationProceedings of the Fifth IASTED International Conference on Modelling, Simulation, and Optimization
Pages125-128
Number of pages4
StatePublished - 1 Dec 2005
Event5th IASTED International Conference on Modelling, Simulation, and Optimization - Oranjestad, Aruba
Duration: 29 Aug 200531 Aug 2005

Publication series

NameProceedings of the IASTED International Conference on Modelling, Simulation, and Optimization
Volume2005

Other

Other5th IASTED International Conference on Modelling, Simulation, and Optimization
CountryAruba
CityOranjestad
Period29/08/0531/08/05

Keywords

  • Gröbner basis
  • Polynomial models
  • Time series

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  • Cite this

    Li, A., & Saydam, S. (2005). Linearality of polynomial models of discrete time series. In Proceedings of the Fifth IASTED International Conference on Modelling, Simulation, and Optimization (pp. 125-128). (Proceedings of the IASTED International Conference on Modelling, Simulation, and Optimization; Vol. 2005).