In this paper we consider the problem of finding a set of monomials O and a polynomial f whose support is contained in O, such that (1) f is almost vanishing at a set of points X whose coordinates are not known exactly and (2) O exhibits structural stability, that is the model/design matrix associated to O is full rank for each set of points differing only slightly from X. We review some numerical versions of the Buchberger- Moller (BM) algorithm for computing the set O and the polynomial f and we present a variant, called LDP-LP, which integrates one of these methods with a classical statistical least squares algorithm for implicit regression from [1]. To illustrate the usefulness of these numerical BM algorithms, we review some of their application in the analyses of data sets for which standard techniques did not yield satisfactory results.

BM algorithms for noisy data and implicit regression modelling

FASSINO, CLAUDIA;RICCOMAGNO, EVA
2017

Abstract

In this paper we consider the problem of finding a set of monomials O and a polynomial f whose support is contained in O, such that (1) f is almost vanishing at a set of points X whose coordinates are not known exactly and (2) O exhibits structural stability, that is the model/design matrix associated to O is full rank for each set of points differing only slightly from X. We review some numerical versions of the Buchberger- Moller (BM) algorithm for computing the set O and the polynomial f and we present a variant, called LDP-LP, which integrates one of these methods with a classical statistical least squares algorithm for implicit regression from [1]. To illustrate the usefulness of these numerical BM algorithms, we review some of their application in the analyses of data sets for which standard techniques did not yield satisfactory results.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/882814
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