A linear algebra approach to the differentiation index of generic DAE systems

The notion of differentiation index for DAE systems of arbitrary order with generic second members is discussed by means of the study of the behavior of the ranks of certain Jacobian associated sub-matrices. As a by-product, we obtain upper bounds for the regularity of the Hilbert-Kolchin function a...

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Detalles Bibliográficos
Autores principales: D'Alfonso, L., Jeronimo, G., Solernó, P.
Formato: JOUR
Materias:
Arbitrary order
Characteristic set
DAE systems
Hilbert
Jacobians
Sub-matrices
Upper Bound
Jacobian matrices
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_09381279_v19_n6_p441_DAlfonso
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_09381279_v19_n6_p441_DAlfonso2023-10-03T15:48:44Z A linear algebra approach to the differentiation index of generic DAE systems D'Alfonso, L. Jeronimo, G. Solernó, P. Arbitrary order Characteristic set DAE systems Hilbert Jacobians Sub-matrices Upper Bound Jacobian matrices The notion of differentiation index for DAE systems of arbitrary order with generic second members is discussed by means of the study of the behavior of the ranks of certain Jacobian associated sub-matrices. As a by-product, we obtain upper bounds for the regularity of the Hilbert-Kolchin function and the order of the ideal associated to the DAE systems under consideration, not depending on characteristic sets. Some quantitative and algorithmic results concerning differential transcendence bases and induced equivalent explicit ODE systems are also established. © 2008 Springer-Verlag. Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Solernó, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09381279_v19_n6_p441_DAlfonso
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Arbitrary order
Characteristic set
DAE systems
Hilbert
Jacobians
Sub-matrices
Upper Bound
Jacobian matrices
spellingShingle Arbitrary order
Characteristic set
DAE systems
Hilbert
Jacobians
Sub-matrices
Upper Bound
Jacobian matrices
D'Alfonso, L.
Jeronimo, G.
Solernó, P.
A linear algebra approach to the differentiation index of generic DAE systems
topic_facet Arbitrary order
Characteristic set
DAE systems
Hilbert
Jacobians
Sub-matrices
Upper Bound
Jacobian matrices
description The notion of differentiation index for DAE systems of arbitrary order with generic second members is discussed by means of the study of the behavior of the ranks of certain Jacobian associated sub-matrices. As a by-product, we obtain upper bounds for the regularity of the Hilbert-Kolchin function and the order of the ideal associated to the DAE systems under consideration, not depending on characteristic sets. Some quantitative and algorithmic results concerning differential transcendence bases and induced equivalent explicit ODE systems are also established. © 2008 Springer-Verlag.
format JOUR
author D'Alfonso, L.
Jeronimo, G.
Solernó, P.
author_facet D'Alfonso, L.
Jeronimo, G.
Solernó, P.
author_sort D'Alfonso, L.
title A linear algebra approach to the differentiation index of generic DAE systems
title_short A linear algebra approach to the differentiation index of generic DAE systems
title_full A linear algebra approach to the differentiation index of generic DAE systems
title_fullStr A linear algebra approach to the differentiation index of generic DAE systems
title_full_unstemmed A linear algebra approach to the differentiation index of generic DAE systems
title_sort linear algebra approach to the differentiation index of generic dae systems
url http://hdl.handle.net/20.500.12110/paper_09381279_v19_n6_p441_DAlfonso
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AT dalfonsol linearalgebraapproachtothedifferentiationindexofgenericdaesystems
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