Mathematics in Computer Science

, Volume 4, Issue 2–3, pp 289–312 | Cite as

Serre’s Reduction of Linear Functional Systems

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Abstract

Serre’s reduction aims at reducing the number of unknowns and equations of a linear functional system. Finding an equivalent presentation of a linear functional system containing fewer equations and fewer unknowns can generally simplify both the study of the structural properties of the linear functional system and of different numerical analysis issues, and it can sometimes help solving the linear functional system. The purpose of this paper is to present a constructive approach to Serre’s reduction for determined and underdetermined linear functional systems.

Keywords

Serre’s reduction Linear functional systems Module theory Homological algebra Symbolic computation Mathematical systems theory 

Mathematics Subject Classification (2010)

Primary 16D70 Secondary 93A10 
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© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Mathematics and Statistics DepartmentSultan Qaboos UniversityMuscatOman
  2. 2.INRIA Saclay - Ile-de-France, DISCO ProjectGif-sur-Yvette cedexFrance

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