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Here are some beginner ones, marking my progress on the understanding of the subject, partially unfinished:
* report3_8: A first glance on the problem -- approximation and estimation [.doc] [.dvi] [.ps] {the reply}
* report3_11: The model in use: IVP for ODE, its Taylor punctual and interval solutions [.doc] [.dvi] [.ps]
* report3_21: Taylor interval solution: soundness proof and residual covering [.doc] [.dvi] [.ps]
* report3_29: Empirical context: thermodynamic diffusion and k-d models for it [.doc] [.dvi] [.ps]
* report4_5: A second glance on the problem -- what is simulation? [.doc] [.dvi] [.ps]
* report4_28: Indirect measurement on a model for conductivity and diffusivity [.doc] [.dvi] [.ps]
* report5_3: General proposition of system modeling and identification: a framework [.doc] [.dvi] [.ps]
* report5_4: Estimation: a little bit of philosophy [.doc] [.dvi] [.ps]
* report5_6: A method for validating set-inversion software and the thermic model in detail [.doc] [.dvi] [.ps]
* 5_17: I've made clear the subject I should implement (to replace EMV by IHO in the prediction, or say, integration step),
a report of my new march?will (should!) be on. [.doc] [.dvi] [.ps]
* 5_25: I've understood the two procedures, namely state and parameter estimations, I will take some time to read
the new paper[5] in order to get into the new and unknown domain of arbitary precision. [.doc] [.dvi] [.ps]
* To appear in the long term: Deterministic modeling | On divergence (I've made it clear)
* 7_19: FIN! sorry for the blanc so long, I concluded the topic into a classical mathematic one, spent a couple of weeks to read things on real analysis.
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Current objective |
* exact calculation of explicit model (see report5_6)
* algorithmic exploration of implicit model (see future! report5_25)
* size problem (detail)
* arbitrary precision
* border limit using analytic ways
% Current research on algorithms are always trying to improve on the ..., is there any other new viewpoints ? %
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References |
* BOOKS AND AUTHORS
[1] Applied Interval Analysis, Luc Jaulin, Eric Walter, Olivier Didrit, Michel Kieffer, Guy Demoment, Jean-Louis Ferrier.
% This book contains a self-contained "motivation-algorithms-application" structure. %
[2] Introduction to Interval Computations, (some German authors)
% This book looks like seminar notes, (1) focused on interval linear algebra; (2) fixpoint resolution of equations;
(3) complex interval analysis; (4) machine implementation. %
[3] Moore 1966, Interval Analysis
[4] Hansen 1965, Interval manipulation in linear algebra
[5] Topics in Interval Analysis, E.Hansen, 1969
% This little book is a joyable text composing two parts: algebraic problems and continuous problems.%
[6] Scientific Computing and Differential Equations -- An introduction to numerical methods, Gene H.Golub, James M. Ortega.
% A gentil book.%
[7]
[8] Global optimization using interval analysis, Eldon Hansen
* THESIS
[1] N.Nedialkov, Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation
[2] (the one in french)
[3] F.N.Ris, Interval Analysis and Applications to Linear Algebra, Oxford 1972
* PAPERS
[1] (the paper on CERTES experiment)
[2] Parameter estimation for non-linear continuous-time systems in a bounded error context, T.Raissi, N.Ramdani, Y.Candau
[3] Caract�risation garantie d'un dispositif de mesure de grandeurs thermiques, I.Braems, N.Ramdani, M.Kieffer, E.Walter
[4] Set membership state and parameter estimation for systems described by nonlinear differential equations, T.Raissi, N.Ramdani, Y.Candau
[5] Guaranteed recursive non-linear state bounding using interval analysis, M.Kieffer, L.Jaulin, E.Walter
* WEB
[1] www.cs.utep.edu/interval-comp/main.html
[2] liinwww.ira.uka.de/bibliography/
* SOFTWARE: VNODE
* COLLEAGUE: Tarek Raissi @, Joseph Bourgeois @, Amir Nakibamir @ ...
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