### 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.

Original language | English |
---|---|

Pages (from-to) | 289-312 |

Number of pages | 24 |

Journal | Mathematics in Computer Science |

Volume | 4 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - Sep 2010 |

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### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Computational Theory and Mathematics

### Cite this

*Mathematics in Computer Science*,

*4*(2-3), 289-312. https://doi.org/10.1007/s11786-010-0057-y

**Serre's Reduction of Linear Functional Systems.** / Boudellioua, M. S.; Quadrat, A.

Research output: Contribution to journal › Article

*Mathematics in Computer Science*, vol. 4, no. 2-3, pp. 289-312. https://doi.org/10.1007/s11786-010-0057-y

}

TY - JOUR

T1 - Serre's Reduction of Linear Functional Systems

AU - Boudellioua, M. S.

AU - Quadrat, A.

PY - 2010/9

Y1 - 2010/9

N2 - 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.

AB - 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.

KW - Homological algebra

KW - Linear functional systems

KW - Mathematical systems theory

KW - Module theory

KW - Serre's reduction

KW - Symbolic computation

UR - http://www.scopus.com/inward/record.url?scp=79952247703&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952247703&partnerID=8YFLogxK

U2 - 10.1007/s11786-010-0057-y

DO - 10.1007/s11786-010-0057-y

M3 - Article

AN - SCOPUS:79952247703

VL - 4

SP - 289

EP - 312

JO - Mathematics in Computer Science

JF - Mathematics in Computer Science

SN - 1661-8270

IS - 2-3

ER -