Simultaneous triangularization of commuting matrices for the solution of polynomial equations

Vanesa Cortés; Juan Peña; Tomas Sauer

Open Mathematics (2012)

  • Volume: 10, Issue: 1, page 277-291
  • ISSN: 2391-5455

Abstract

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We present an extension of the QR method to simultaneously compute the joint eigenvalues of a finite family of commuting matrices. The problem is motivated by the task of finding solutions of a polynomial system. Several examples are included.

How to cite

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Vanesa Cortés, Juan Peña, and Tomas Sauer. "Simultaneous triangularization of commuting matrices for the solution of polynomial equations." Open Mathematics 10.1 (2012): 277-291. <http://eudml.org/doc/269622>.

@article{VanesaCortés2012,
abstract = {We present an extension of the QR method to simultaneously compute the joint eigenvalues of a finite family of commuting matrices. The problem is motivated by the task of finding solutions of a polynomial system. Several examples are included.},
author = {Vanesa Cortés, Juan Peña, Tomas Sauer},
journal = {Open Mathematics},
keywords = {QR-method; Commuting matrices; Simultaneous triangularization; commuting matrices; simultaneous triangularization; numerical examples; joint eigenvalues; polynomial system},
language = {eng},
number = {1},
pages = {277-291},
title = {Simultaneous triangularization of commuting matrices for the solution of polynomial equations},
url = {http://eudml.org/doc/269622},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Vanesa Cortés
AU - Juan Peña
AU - Tomas Sauer
TI - Simultaneous triangularization of commuting matrices for the solution of polynomial equations
JO - Open Mathematics
PY - 2012
VL - 10
IS - 1
SP - 277
EP - 291
AB - We present an extension of the QR method to simultaneously compute the joint eigenvalues of a finite family of commuting matrices. The problem is motivated by the task of finding solutions of a polynomial system. Several examples are included.
LA - eng
KW - QR-method; Commuting matrices; Simultaneous triangularization; commuting matrices; simultaneous triangularization; numerical examples; joint eigenvalues; polynomial system
UR - http://eudml.org/doc/269622
ER -

References

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