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}}

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}}

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}}

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}}