NDLI: Exact linear modeling with polynomial coefficients

Content Provider	Springer Nature Link
Author	Zerz, Eva Levandovskyy, Viktor Schindelar, Kristina
Copyright Year	2010
Abstract	Given a finite set of polynomial, multivariate, and vector-valued functions, we show that their span can be written as the solution set of a linear system of partial differential equations (PDE) with polynomial coefficients. We present two different but equivalent ways to construct a PDE system whose solution set is precisely the span of the given trajectories. One is based on commutative algebra and the other one works directly in the Weyl algebra, thus requiring the use of tools from non-commutative computer algebra. In behavioral systems theory, the resulting model for the data is known as the most powerful unfalsified model (MPUM) within the class of linear systems with kernel representations over the Weyl algebra, i.e., the ring of differential operators with polynomial coefficients.
Starting Page	55
Ending Page	65
Page Count	11
File Format	PDF
ISSN	09236082
Journal	Multidimensional Systems and Signal Processing
Volume Number	22
Issue Number	1-3
e-ISSN	15730824
Language	English
Publisher	Springer US
Publisher Date	2010-07-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Multidimensional systems Linear systems with polynomial coefficients Behavioral approach Linear exact modeling Polynomial trajectories Most powerful unfalsified model Gröbner bases Artificial Intelligence (incl. Robotics) Signal, Image and Speech Processing Electrical Engineering Circuits and Systems
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Signal Processing Information Systems Computer Science Applications Software Hardware and Architecture

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