An algebraic method for multi-dimensional derivative estimation

Author

Riachy, Samer ; Bachalany, Yara ; Mboup, Mamadou ; Richard, Jean-Pierre

Author_Institution

LAGIS, Ecole Centrale de Lille, Villeneuve-d´´Ascq

fYear

2008

fDate

25-27 June 2008

Firstpage

356

Lastpage

361

Abstract

This communication revisits the algebra-based results for derivative estimation presented by Fliess and coauthors in 2005. It is proposed, here, to consider multidimensional functions, namely scalar or vector fields of several variables. Such fields are locally represented by a vector Taylor series expansion, and a computation technique is presented so to express successive partial derivatives (for instance, the gradient, the Hessian matrix...) as functions of iterated integrals of the measured quantities.

Keywords

differentiation; integration; iterative methods; multidimensional signal processing; series (mathematics); vectors; algebraic method; iterated integral; multidimensional partial derivative estimation; multidimensional signal processing; numerical differentiation; numerical integration; scalar field; vector Taylor series expansion; vector field; Automatic control; Automation; Communication system control; Heat transfer; Image edge detection; Laplace equations; Mathematics; Multidimensional systems; Numerical simulation; Taylor series;

fLanguage

English

Publisher

ieee

Conference_Titel

Control and Automation, 2008 16th Mediterranean Conference on

Conference_Location

Ajaccio

Print_ISBN

978-1-4244-2504-4

Electronic_ISBN

978-1-4244-2505-1

Type

conf

DOI

10.1109/MED.2008.4602167

Filename

4602167