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### Annuaire

Consultant
Algorithmes parallèles
05 61 19 30 26
Francoise.Chatelin@cerfacs.fr

# @ARTICLE

Chatelin, F. and Rincon-Camacho, M.M. (2017) Hermitian matrices: Spectral coupling, plane geometry / trigonometry and optimisation, Linear Algebra and its Applications, 553, pp. 282-310
[bibtex] [pdf]

@ARTICLE{AR-PA-17-162, author = {Chatelin, F. and Rincon-Camacho, M.M. }, title = {Hermitian matrices: Spectral coupling, plane geometry / trigonometry and optimisation}, year = {2017}, volume = {553}, pages = {282-310}, journal = {Linear Algebra and its Applications}, abstract = {The paper presents the information processing that can be performed by a general hermitian matrix when two of its distinct eigenvalues are coupled, such as λ<λ′, instead of considering only one eigenvalue as traditional spectral theory does. Setting a=λ+λ′2≠0 and e=λ′−λ2>0, the information is delivered in geometric form, both metric and trigonometric, associated with various right-angled triangles exhibiting optimality properties quantified as ratios or product of |a| and e. The potential optimisation has a triple nature which offers two possibilities: in the case λλ′>0 they are characterised by e|a| and |a|e and in the case λλ′<0 by |a|e and |a|e. This nature is revealed by a key generalisation to indefinite matrices over R or C of Gustafson's operator trigonometry.}, keywords = {Spectral coupling,Indefinite symmetric or hermitian matrix,Spectral plane,Invariant plane,Catchvector,Antieigenvector,Midvector,Local optimisation,Euler equation,Balance equation,Torus in 3D,Angle between complex lines}, pdf = {https://doi.org/10.1016/j.laa.2017.07.009}, supplementaryMaterial = {http://www.cerfacs.fr/algor/reports/2015/TR_PA_15_31.pdf}}

Chatelin, F. (2016) The principle of relativity from Ungar's gyrolanguage for physics to weaving computation in mathematics, Mathematics Interdisciplinary Research, 1 (1) , pp. 199-228
[bibtex] [url]

@ARTICLE{AR-PA-16-2, author = {Chatelin, F. }, title = {The principle of relativity from Ungar's gyrolanguage for physics to weaving computation in mathematics}, year = {2016}, number = {1}, volume = {1}, pages = {199-228}, journal = {Mathematics Interdisciplinary Research}, url = {http://mir.kashanu.ac.ir/article_13924_d4a841bd69d5a2c5caa9b2def6a387cb.pdf}}

Chatelin, F. (2013) About weaving computation in 2 and 3 dimensions, International Journal of Unconventional Computing, 9 (1) , pp. 37-59
[bibtex]

@ARTICLE{AR-PA-13-28075, author = {Chatelin, F. }, title = {About weaving computation in 2 and 3 dimensions}, year = {2013}, number = {1}, volume = {9}, pages = {37-59}, journal = {International Journal of Unconventional Computing}}

Chatelin, F. (2012) A computational journey into the mind, Natural Computing, 11, pp. 67-79
[bibtex]

@ARTICLE{AR-PA-12-28115, author = {Chatelin, F. }, title = {A computational journey into the mind}, year = {2012}, volume = {11}, pages = {67-79}, journal = {Natural Computing}}

Calude, C.S. and Chatelin, F. (2010) A dialogue about qualitative computing, Bulletin of the European Association for Theoretical Computer Science, 101, pp. 29-41, ISSN 0252 – 9742
[bibtex] [url]

@ARTICLE{AR-PA-10-19632, author = {Calude, C.S. and Chatelin, F. }, title = {A dialogue about qualitative computing}, year = {2010}, volume = {101}, pages = {29-41}, issn = {0252 – 9742}, journal = {Bulletin of the European Association for Theoretical Computer Science}, url = {http://www.cerfacs.fr/algor/reports/2010/TR_PA_10_37.pdf}}

Chatelin, F. (2010) Numerical information processing under the global rule expressed by the Euler-Riemann ζ function defined in the complex plane, 20 (3) , doi: 10.1063/1.3489917
[bibtex] [url] [pdf]

@ARTICLE{AR-PA-10-19685, author = {Chatelin, F. }, title = {Numerical information processing under the global rule expressed by the Euler-Riemann ζ function defined in the complex plane}, year = {2010}, number = {3}, volume = {20}, doi = {10.1063/1.3489917}, pdf = { http://dx.doi.org/10.1063/1.3489917}, url = {http://www.cerfacs.fr/algor/reports/2010/TR_PA_10_49.pdf}}

# @CONFERENCE

Chatelin, F. (1993) The influence of nonnormality on matrix computations, Linear algebra, markov chains and queueing models. 1993
[bibtex]

@conference{PR-PA-93-19675, author = {Chatelin, F. }, title = {The influence of nonnormality on matrix computations}, year = {1993}, pages = {13 - 19}, booktitle = {Linear algebra, markov chains and queueing models}}

Chatelin, F. and Frayssé, V. (1992) Elements of a condition theory for the computational analysis of algorithms, Iterative methods in linear algebra. 1992
[bibtex]

@conference{PR-PA-92-19712, author = {Chatelin, F. and Frayss´{e}, V. }, title = {Elements of a condition theory for the computational analysis of algorithms}, year = {1992}, pages = {15 - 25}, booktitle = {Iterative methods in linear algebra}}

Chatelin, F. and Godet-Thobie, S. (1991) Stability analysis in the aeronautical industry II, 2nd Symposium on High Performance Computing. 1991
[bibtex]

@conference{PR-PA-91-19709, author = {Chatelin, F. and Godet-Thobie, S. }, title = {Stability analysis in the aeronautical industry II}, year = {1991}, pages = {415 - 422}, booktitle = {2nd Symposium on High Performance Computing}}

Chatelin, F. and Frayssé, V. (1991) Arithmetic reliability of algorithms, 2nd Symposium on High Performance Computing. 1991
[bibtex]

@conference{PR-PA-91-19710, author = {Chatelin, F. and Frayss´{e}, V. }, title = {Arithmetic reliability of algorithms}, year = {1991}, pages = {441 - 450}, booktitle = {2nd Symposium on High Performance Computing}}

Chatelin, F. and Frayssé, V. (1991) Analysis of arithmetic algorithms: a statistical study, 10th symposium on computer arithmetic. 1991
[bibtex]

@conference{PR-PA-91-19711, author = {Chatelin, F. and Frayss´{e}, V. }, title = {Analysis of arithmetic algorithms: a statistical study}, year = {1991}, pages = {10 - 16}, booktitle = {10th symposium on computer arithmetic}}

# @BOOK

Chatelin, F. (2015) Qualitative Computing in the book "The Human Face of Computing", C. S. Calude, p.183-202
[bibtex] [url]

@BOOK{BK-PA-15-24983, author = {Chatelin, F. }, title = {Qualitative Computing in the book "The Human Face of Computing"}, year = {2015}, publisher = {C. S. Calude}, chapter = {13}, volume = {9}, pages = {183-202}, month = {9}, url = {http://www.worldscientific.com/worldscibooks/10.1142/p992}}

Chatelin, F. (2012) Qualitative Computing: A computational journey into nonlinearity, World Scientific Publishing Co Pte Ltd
[bibtex]

@BOOK{BK-PA-12-28140, author = {Chatelin, F. }, title = {Qualitative Computing: A computational journey into nonlinearity}, year = {2012}, publisher = {World Scientific Publishing Co Pte Ltd}, isbn = {978-981-4322-92-8 }, month = {8}}

Chatelin, F. (2012) Eigenvalues of matrices : Revised Edition, SIAM
[bibtex] [url]

@BOOK{BK-PA-12-28142, author = {Chatelin, F. }, title = {Eigenvalues of matrices : Revised Edition}, year = {2012}, publisher = {SIAM}, isbn = {978-1-61197-245-0}, url = {http://dx.doi.org/10.1137/1.9781611972467}}

Chatelin, F. (1993) Eigenvalues of matrices, Enlarged Translation
[bibtex]

@book{BK-PA-93-19688, author = {Chatelin, F. }, title = {Eigenvalues of matrices}, year = {1993}, publisher = {Enlarged Translation}}

# @TECHREPORT

Chatelin, F. and Rincon-Camacho, M.M. (2016) Spectral Coupling for Hermitian Matrices, Cerfacs, technical report
[bibtex] [pdf]

@TECHREPORT{TR-PA-16-240, author = {Chatelin, F. and Rincon-Camacho, M.M. }, title = {Spectral Coupling for Hermitian Matrices}, year = {2016}, institution = {Cerfacs}, month = {10}, type = {technical report}, pdf = {https://cerfacs.fr/wp-content/uploads/2016/12/technical_report_16-240_spectral_coupling.pdf}}

Chatelin, F. (2015) Differential information processing in the light of quaternions, Cerfacs, Toulouse, France, technical report
[bibtex] [url]

@techreport{TR-PA-15-19676, author = {Chatelin, F. }, title = {Differential information processing in the light of quaternions}, year = {2015}, institution = {{Cerfacs}, Toulouse, France}, type = {technical report}, url = {http://www.cerfacs.fr/algor/reports/2015/TR_PA_15_7.pdf}}

Chatelin, F. and Rincon-Camacho, M.M. (2015) Symmetric and hermitian matrices : a geometric perspective on spectral coupling, technical report
[bibtex] [url]

@TECHREPORT{TR-PA-15-24099, author = {Chatelin, F. and Rincon-Camacho, M.M. }, title = {Symmetric and hermitian matrices : a geometric perspective on spectral coupling}, year = {2015}, month = {7}, type = {technical report}, abstract = {The report develops the information processing begin in TR/PA/15/31 that can be performed by a general hermitian matrix when two of its distinct eigenvalues are coupled, such as $\lambda < \lambda'$. Setting $a = \frac{\lambda + \lambda'}{2}$ and $e = \frac{\lambda'-\lambda}{2} > 0$, the new spectral information that is provided by coupling is expressed in terms of the ratios $\frac{e}{|a|}$ (if $\lambda \lambda' > 0$) or $\frac{|a|}{e}$ (if $\lambda \lambda' < 0$) and of the product $|a| e$. The information is delivered in geometric form, both metric and trigonometric, associated with various right-angled triangles deriving from optimality conditions. The paper contains a generalisation to indefinite matrices over $\mathbb{R}$ or $\mathbb{C}$ of Gustafson's operator trigonometry which in the matrix case assumes definiteness (mostly over $\mathbb{R}$).}, url = {https://cerfacs.fr/wp-content/uploads/2015/09/TR_PA_15_56.pdf}}

Chatelin, F. (2014) A dialogue with cris calude about qualitative computing, Cerfacs, Toulouse, France, technical report
[bibtex] [url]

@techreport{TR-PA-14-19677, author = {Chatelin, F. }, title = {A dialogue with cris calude about qualitative computing}, year = {2014}, institution = {{Cerfacs}, Toulouse, France}, type = {technical report}, url = {http://www.cerfacs.fr/algor/reports/2014/TR_PA_14_56.pdf}}

Chatelin, F., Latre, J.B., Rincon-Camacho, M.M. and Ricoux, P. (2014) Beyond and behind linear algebra, Cerfacs, Toulouse, France, technical report
[bibtex] [url]

@techreport{TR-PA-14-19701, author = {Chatelin, F. and Latre, J.B. and Rincon-Camacho, M.M. and Ricoux, P. }, title = {Beyond and behind linear algebra}, year = {2014}, institution = {{Cerfacs}, Toulouse, France}, type = {technical report}, url = {http://www.cerfacs.fr/algor/reports/2014/TR_PA_14_80.pdf}}

Rincon-Camacho, M.M., Chatelin, F. and Ricoux, P. (2014) About a family of logistic equations based on a relative distance to 1/2 raised to a positive power, Cerfacs, Toulouse, France, technical report
[bibtex] [url]

@techreport{TR-PA-14-20136, author = {Rincon-Camacho, M.M. and Chatelin, F. and Ricoux, P. }, title = {About a family of logistic equations based on a relative distance to 1/2 raised to a positive power}, year = {2014}, institution = {{Cerfacs}, Toulouse, France}, type = {technical report}, url = {http://www.cerfacs.fr/algor/reports/2014/TR_PA_14_55.pdf}}

Rincon-Camacho, M.M., Chatelin, F. and Ricoux, P. (2014) Beyond boolean logic.a family of logistic equations as a model for numerical evolution of the fixed points 0 and 1 for multiplication, Cerfacs, Toulouse, France, technical report
[bibtex] [url]

@techreport{TR-PA-14-20137, author = {Rincon-Camacho, M.M. and Chatelin, F. and Ricoux, P. }, title = {Beyond boolean logic.a family of logistic equations as a model for numerical evolution of the fixed points 0 and 1 for multiplication}, year = {2014}, institution = {{Cerfacs}, Toulouse, France}, type = {technical report}, url = {http://www.cerfacs.fr/algor/reports/2014/TR_PA_14_68.pdf}}

Rincon-Camacho, M.M., Chatelin, F. and Ricoux, P. (2014) About relative and absolute logic evolutions under laws of degree 2 and 4 and in 4 dimensions at most, Cerfacs, Toulouse, France, technical report
[bibtex] [url]

@techreport{TR-PA-14-20138, author = {Rincon-Camacho, M.M. and Chatelin, F. and Ricoux, P. }, title = {About relative and absolute logic evolutions under laws of degree 2 and 4 and in 4 dimensions at most}, year = {2014}, institution = {{Cerfacs}, Toulouse, France}, type = {technical report}, url = {http://www.cerfacs.fr/algor/reports/2014/TR_PA_14_75.pdf}}

Chatelin, F. (2012) Computation in mind, Cerfacs, Toulouse, France, technical report
[bibtex] [url]

@techreport{TR-PA-12-19678, author = {Chatelin, F. }, title = {Computation in mind}, year = {2012}, institution = {{Cerfacs}, Toulouse, France}, type = {technical report}, url = {http://www.cerfacs.fr/algor/reports/2012/TR_PA_12_15.pdf}}

Chatelin, F. (2011) Polymorphic information processing in weaving computation: an approach through cloth geometry, Cerfacs, Toulouse, France, technical report
[bibtex] [url]

@techreport{TR-PA-11-19679, author = {Chatelin, F. }, title = {Polymorphic information processing in weaving computation: an approach through cloth geometry}, year = {2011}, institution = {{Cerfacs}, Toulouse, France}, type = {technical report}, url = {http://www.cerfacs.fr/algor/reports/2011/TR_PA_11_27.pdf}}

Chatelin, F. (2011) On relating computation, Cerfacs, Toulouse, France, technical report
[bibtex] [url]

@techreport{TR-PA-11-19680, author = {Chatelin, F. }, title = {On relating computation}, year = {2011}, institution = {{Cerfacs}, Toulouse, France}, type = {technical report}, url = {http://www.cerfacs.fr/algor/reports/2011/TR_PA_11_37.pdf}}

Chatelin, F. (2011) An invitation to qualitative computing, Cerfacs, Toulouse, France, technical report
[bibtex] [url]

@techreport{TR-PA-11-19681, author = {Chatelin, F. }, title = {An invitation to qualitative computing}, year = {2011}, institution = {{Cerfacs}, Toulouse, France}, type = {technical report}, url = {http://www.cerfacs.fr/algor/reports/2011/TR_PA_11_38.pdf}}

Chatelin, F. (2011) A computational journey into the mind, Cerfacs, Toulouse, France, technical report
[bibtex] [url]

@techreport{TR-PA-11-19682, author = {Chatelin, F. }, title = {A computational journey into the mind}, year = {2011}, institution = {{Cerfacs}, Toulouse, France}, type = {technical report}, url = {http://www.cerfacs.fr/algor/reports/2011/TR_PA_11_66.pdf}}

Chatelin, F. (2011) About weaving computation in $2$ and $3$ real dimensions, Cerfacs, Toulouse, France, technical report
[bibtex] [url]

@techreport{TR-PA-11-19683, author = {Chatelin, F. }, title = {About weaving computation in $2$ and $3$ real dimensions}, year = {2011}, institution = {{Cerfacs}, Toulouse, France}, type = {technical report}, url = {http://www.cerfacs.fr/algor/reports/2011/TR_PA_11_119.pdf}}

Chatelin, F. (2010) A computational journey into nonlinearity, Cerfacs, Toulouse, France, technical report
[bibtex] [url]

@techreport{TR-PA-10-19684, author = {Chatelin, F. }, title = {A computational journey into nonlinearity}, year = {2010}, institution = {{Cerfacs}, Toulouse, France}, type = {technical report}, url = {http://www.cerfacs.fr/algor/reports/2010/TR_PA_10_38.pdf}}

Chatelin, F. (2010) A computational journey into nonlinearity, Cerfacs, Toulouse, France, technical report
[bibtex] [url]

@techreport{TR-PA-10-19686, author = {Chatelin, F. }, title = {A computational journey into nonlinearity}, year = {2010}, institution = {{Cerfacs}, Toulouse, France}, type = {technical report}, url = {http://www.cerfacs.fr/algor/reports/2010/TR_PA_10_109.pdf}}

Braconnier, T., Chatelin, F. and Frayssé, V. (1993) Qualitative Computing, : elements of a theory for finite precision computation, Cerfacs, technical report
[bibtex]

@techreport{TR-PA-93-20352, author = {Braconnier, T. and Chatelin, F. and Frayss´{e}, V. }, title = {Qualitative Computing, : elements of a theory for finite precision computation}, year = {1993}, institution = {Cerfacs}, type = {technical report}}

Chatelin, F. and Frayssé, V. (1991) A statistical study of the stability of linear systems, Cerfacs, technical report
[bibtex]

@techreport{TR-PA-91-19713, author = {Chatelin, F. and Frayss´{e}, V. }, title = {A statistical study of the stability of linear systems}, year = {1991}, institution = {Cerfacs}, type = {technical report}}

Chatelin, F. and Frayssé, V. (1991) Arithmetic reliability of algorithms, Cerfacs
[bibtex]

@techreport{TR-PA-91-19714, author = {Chatelin, F. and Frayss´{e}, V. }, title = {Arithmetic reliability of algorithms}, year = {1991}, institution = {Cerfacs}}

Chatelin, F. and Frayssé, V. (1991) Analysis of arithmetic algorithms: a statistical study, Cerfacs
[bibtex]

@techreport{TR-PA-91-19715, author = {Chatelin, F. and Frayss´{e}, V. }, title = {Analysis of arithmetic algorithms: a statistical study}, year = {1991}, institution = {Cerfacs}}

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