R. Abraham and J. Marsden, Foundations of Mechanics, 1978.

V. I. Arnold, Mathematical Methods of Classical Mechanics, 1978.

R. Adler, J. Dedieu, J. Margulies, M. Martens, and M. Shub, Newton Method on Riemannian Manifolds and a Geometric Model for the Human Spine, IMA Journal of Numerical Analysis, pp.22-23, 2002.

E. Celledoni and A. Iserles, Methods for the approximation of the matrix exponential in a Lie-algebraic setting, IMA Journal of Numerical Analysis, vol.21, issue.2, pp.463-488, 2001.
DOI : 10.1093/imanum/21.2.463

J. Dedieu and M. Shub, Multihomogeneous Newton methods, Mathematics of Computation, vol.69, issue.231, pp.1071-1098, 2000.
DOI : 10.1090/S0025-5718-99-01114-X
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.3939

J. Dieudonné, Treatise on Analysis, 1988.

A. Edelman, T. Arias, and S. Smith, The Geometry of Algorithms with Orthogonality Constraints, SIAM Journal on Matrix Analysis and Applications, vol.20, issue.2, pp.303-353, 1998.
DOI : 10.1137/S0895479895290954

O. Ferreira and B. Svaiter, Kantorovich's Theorem on Newton's Method in Riemannian Manifolds, Journal of Complexity, vol.18, issue.1, pp.304-329, 2002.
DOI : 10.1006/jcom.2001.0582

C. A. Floudas and . Pardolos, Handbook of test problems in local and global optimization, 1999.
DOI : 10.1007/978-1-4757-3040-1

E. Hairer, Global modified Hamiltonian for constrained symplectic integrators, Numerische Mathematik, vol.95, issue.2, pp.325-336, 2003.
DOI : 10.1007/s00211-002-0428-7

E. Hairer and C. Lubich, The life-span of backward error analysis for numerical integrators, Numerische Mathematik, vol.76, issue.4, pp.325-336, 1997.
DOI : 10.1007/s002110050271

E. Hairer, S. P. Norsett, and G. Wanner, Solving ordinary differential equations. I. Nonstiff problems, 1993.

K. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, 1979.
DOI : 10.1090/gsm/034

A. Iserles, On Cayley-Transform Methods for the Discretization of Lie-Group Equations, Foundations of Computational Mathematics, vol.1, issue.2, pp.129-160, 2001.
DOI : 10.1007/s102080010003

A. Iserles, H. Z. Munthe-kaas, S. P. Nørset, and A. Zanna, Lie-group methods, Liegroup methods, pp.215-365, 2001.
DOI : 10.1017/S0962492900002154
URL : https://hal.archives-ouvertes.fr/hal-01328729

S. Katsura and M. Sasaki, The asymmetric continuous distribution function of the effective field of the Ising model in the spin glass and the ferromagnetic states on the Bethe lattice, Physica A, vol.1573, pp.1195-1202, 1989.

S. Krogstad, H. Munthe-kaas, and A. Zanna, Generalized polar coordinates on Lie groups and numerical integrators, Numerische Mathematik, vol.175, issue.1, 2003.
DOI : 10.1007/s00211-009-0255-1

G. Malajovich, On generalized Newton algorithms: quadratic convergence, path-following and error analysis, Theoretical Computer Science, vol.133, issue.1, pp.65-84, 1994.
DOI : 10.1016/0304-3975(94)00065-4

J. Marsden and T. Ratiu, Introduction to Mechanics and Symmetry, 1994.
DOI : 10.1007/978-1-4612-2682-6
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.369.5772

H. Z. Munthe-kaas, G. R. Quispel, and A. Zanna, Generalized polar decompositions on Lie groups with involutive automorphisms, Found, Comput. Math, vol.1, pp.297-324, 2001.

B. Owren and B. Welfert, The Newton Iteration on Lie Groups, Bit Numerical Mathematics, vol.40, issue.1, pp.121-145, 2000.
DOI : 10.1023/A:1022322503301

M. Shub, Some Remarks on Dynamical Systems and Numerical Analysis, in: Dynamical Systems and Partial Differential Equations, Proceedings of VII ELAM (L. Lara-Carrero and J. Lewowicz eds.), Equinoccio, pp.69-92, 1986.

M. Shub, Some Remarks on Bezout's Theorem and Complexity, in From Topology to Computation: Proceedings of the, pp.443-455, 1993.

M. Shub and S. Smale, Complexity of Bézout's Theorem I: Geometric Aspects, J. Am. Math. Soc, pp.459-501, 1993.

M. Shub and S. Smale, Complexity of Bezout???s Theorem IV: Probability of Success; Extensions, SIAM Journal on Numerical Analysis, vol.33, issue.1, pp.128-148, 1996.
DOI : 10.1137/0733008

M. Shub and S. Smale, Complexity of Bezout's theorem V: polynomial time, Theoretical Computer Science, vol.133, issue.1, pp.141-164, 1994.
DOI : 10.1016/0304-3975(94)90122-8

S. Smith, Optimization techniques on Riemannian manifolds, pp.113-146, 1994.
DOI : 10.1090/fic/003/09
URL : http://arxiv.org/abs/1407.5965

C. Udriste, Convex Functions and Optimization Methods on Riemannian Manifolds, Kluwer, 1994.

A. Zanna and H. Z. , Generalized Polar Decompositions for the Approximation of the Matrix Exponential, SIAM Journal on Matrix Analysis and Applications, vol.23, issue.3, pp.840-862, 2001.
DOI : 10.1137/S0895479800377551

L. Personnaz, I. Guyon, and G. Dreyfus, Collective computational properties of neural networks: New learning mechanisms, Physical Review A, vol.34, issue.5, pp.4217-4228, 1986.
DOI : 10.1103/PhysRevA.34.4217

A. Reznik and . Non-, Non-iterative learning for neural networks, IJCNN'99. International Joint Conference on Neural Networks. Proceedings (Cat. No.99CH36339), 1998.
DOI : 10.1109/IJCNN.1999.831163

S. L. Smale, I. Personnaz, G. Guyon, . O. Dreyfus4-]-d, A. M. Gorodnichy et al., Collective computational properties of neural networks: New learning mechanisms Increasing Attraction of Pseudo- Inverse Neural Networks [5] A. Albert, Regression and the Moore-Penrose pseudoinverse Applied mathematics for engineers and physicists The multifunctional neural computer NeuroLand Storage Capacity of Kernel Associative Memories, On the Mathematical Foundations of Learning Bull. Am. Math. Soc. Proceedings of the Int. Conf. on Inductive Simulation Proceedings of the Int. Conf. on Art. Neural Networks, pp.1-49, 1958.

J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci, pp.2554-2558, 1982.

M. Weinfield, A Fully Digital Integrated CMOS Hopfield Network Including the Learning Algorithm, Proc. Int. Workshop WLSI Art. Intell., Univ. of Oxford, pp.1-10, 1988.
DOI : 10.1007/978-1-4613-1619-0_15

A. M. Reznik, D. O. Gorodnichy, and A. S. Sitchov, Local feedback adjustment in neural networks with projection learning algorithm, Cybernetics and Systems Analysis, vol.6, issue.No. 5, pp.868-875, 1996.
DOI : 10.1007/BF02366866

A. Reznik, Non-iterative learning for neural networks, IJCNN'99. International Joint Conference on Neural Networks. Proceedings (Cat. No.99CH36339), 1999.
DOI : 10.1109/IJCNN.1999.831163

A. S. Sitchov, Weight selection in neural networks with pseudoinverse learning rule, Russian) Mathematical Machines and Systems, pp.25-30, 1998.

A. L. Benabid, B. Wallace, J. Mitrofanis, R. Xia, B. Piallat et al., A putative generalized model of the effects and mechanism of action of High Frequency Electrical Stimulation of the Central Nervous System, Acta neurol. Belg, vol.105, pp.149-157, 2005.
URL : https://hal.archives-ouvertes.fr/inserm-00390985

C. C. Mcintyre, W. M. Grill, D. L. Sherman, and N. V. Thakor, Cellular Effects of Deep Brain Stimulation: Model-Based Analysis of Activation and Inhibition, Journal of Neurophysiology, vol.91, issue.4, pp.1457-1469, 2004.
DOI : 10.1152/jn.00989.2003

R. Roby and E. Lettich, A simplified circuit for stimulus artifact suppression, Electroencephalography and Clinical Neurophysiology, vol.39, issue.1, pp.85-92, 1975.
DOI : 10.1016/0013-4694(75)90130-3

M. Knaflitz and R. Merletti, Suppression of stimulation artifacts from myoelectric-evoked potential recordings, IEEE Transactions on Biomedical Engineering, vol.35, issue.9, pp.758-63, 1988.
DOI : 10.1109/10.7278

M. Solomonow, R. Baratta, T. Miwa, H. Shoji, D. Ambrosia et al., A technique for recording the EMG of electrically stimulated skeletal muscle, J. Orthoped, vol.8, issue.4, pp.492-497, 1985.

E. Roskar and A. Roskar, Microcomputer based electromyographic recording system with stimulus artefact suppression, Third Medical Conference on Biomedical Engineering, 1983.

L. Rossi, G. Foffani, S. Marceglia, F. Bracchi, S. Barbieri et al., An electronic device for artefact suppression in human local field potential recordings during deep brain stimulation, Journal of Neural Engineering, vol.4, issue.2, pp.96-106, 2007.
DOI : 10.1088/1741-2560/4/2/010

T. Blogg and W. Reid, A digital technique for stimulus artifact reduction, Electroencephalography and Clinical Neurophysiology, vol.76, issue.6, pp.557-61, 1990.
DOI : 10.1016/0013-4694(90)90005-5

T. Winchman, A digital averaging method for removal of stimulus artifacts in neurophysiologic experiments, Journal of Neuroscience Methods, vol.98, issue.1, pp.57-62, 2000.
DOI : 10.1016/S0165-0270(00)00190-4

D. A. Wagenaar and . M. Potter-s, Real-time multi-channel stimulus artifact suppression by local curve fitting -DA, J. Neurosci. Methods, 2002.
DOI : 10.1016/s0165-0270(02)00149-8
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.1749

T. Derek, G. M. O-'keeffe, A. E. Lyons, C. A. Donnelly, and . Byrne, Stimulus artifact removal using a software-based two-stage peak detection algorithm, Journal of Neuroscience Methods, vol.109, pp.137-145, 2001.

A. Hines, P. Crago, G. Chapman, and C. Billian, Stimulus artifact removal in EMG from muscles adjacent to stimulated muscles, Journal of Neuroscience Methods, vol.64, issue.1, pp.55-62, 1996.
DOI : 10.1016/0165-0270(95)00099-2

T. Hashimoto, C. M. Elder, M. S. Okun, S. K. Patrick, and J. L. Vitek, Stimulation of the subthalamic nucleus changes the firing pattern of pallidal neurons, J.Neurosci, vol.23, pp.1916-1923, 2003.

T. Hashimoto, C. Elder, and J. Vitek, A template subtraction method for stimulus artifact removal in high-frequency deep brain stimulation, Journal of Neuroscience Methods, vol.113, issue.2, pp.181-186, 2002.
DOI : 10.1016/S0165-0270(01)00491-5

C. Tai, T. Boraud, E. Bezard, B. Bioulac, C. Gross et al., Electrophysiological and metabolic evidence that high-frequency stimulation of the subthalamic nucleus bridles neuronal activity in the subthalamic nucleus and the substantia nigra reticulata, The FASEB Journal, vol.17, issue.13
DOI : 10.1096/fj.03-0163com

L. I. Gudzenko, Statistical method for self-oscillating system characteristics detection, Izvestiia Vuzov Radiophysics, pp.573-587, 1962.

A. E. Villa, An unsupervised automatic method for sorting neuronal spike waveforms in awake and freely moving animals, References [1] P.E. Keller, Overview of electronic nose algorithms Proceedings of the International Joint Conference on Neural Networks, pp.178-187, 1999.

J. W. Gardner and P. N. Bartlett, Electronic Noses, Principles and Applications, 1999.

V. Vapnik, Statistical Learning Theory, p.736, 1998.

S. Haykin, Neural Networks: A Comprehensive Foundation, p.842, 1999.

I. V. Kruglenko, B. A. Snopok, Y. M. Shirshov, and E. F. Venger, Digital aroma technology for chemical sensing: temporal chemical images of complex mixtures, Semicond. Phys., Quant. Electron. Optoelectron, vol.3, issue.4, pp.529-541, 2000.

A. M. Reznik, Y. M. Shirshov, B. A. Snopok, D. W. Nowicki, A. K. Dekhtyarenko et al., Associative memories for chemical sensing, Proceedings of the 9th International Conference on Neural Information Processing, 2002. ICONIP '02., 2002.
DOI : 10.1109/ICONIP.2002.1201972

A. M. Reznik, A. A. Galinskaya, and K. M. , On the information density of Gaussian components used for the classification of ultrasonic location signals, Proceedings of the Eighth All-Russian Conference on Neurocomputers and Their Applications, pp.21-22, 2002.

Z. Boger, R. Cavicchi, and S. Semancik, Analysis of conductometric microsensor responses in 36-sensor array by artificial neural networks modeling, Proceedings of the International Symposium on ISOEN'02, 2002.

P. E. Keller, Overview of electronic nose algorithms, IJCNN'99. International Joint Conference on Neural Networks. Proceedings (Cat. No.99CH36339), 1999.
DOI : 10.1109/IJCNN.1999.831508

A. M. Reznik, Non-iterative learning for neural networks, IJCNN'99. International Joint Conference on Neural Networks. Proceedings (Cat. No.99CH36339), 1999.
DOI : 10.1109/IJCNN.1999.831163

I. V. Kruglenko, B. A. Snopok, Y. M. Shirshov, and E. F. Venger, Digital aroma technology for chemical sensing: temporal chemical images of complex mixtures // Semiconductor Physics, Quantum Electronics&Optoelectronics ?, pp.529-541, 2000.

P. D. Wasserman, Neural computing. Theory and practice, ANZA Research Inc. VAN NOSTRAD REIHOLD, 1988.

N. F. Kirichenko, R. A. Schetenyuk, and S. P. , Matrix pseudo-inversion in the problem of design of associative memory, Cybernetics and Systems Analysis, vol.37, issue.3, pp.308-316, 2001.
DOI : 10.1023/A:1011929525015