L. Albera, A. Ferreol, P. Comon, and P. Chevalier, Blind Identification of Overcomplete MixturEs of sources (BIOME), Linear Algebra and its Applications, vol.391, pp.1-30, 2004.
DOI : 10.1016/j.laa.2004.05.007

URL : https://hal.archives-ouvertes.fr/hal-00536010

J. Alexander and A. Hirschowitz, La m???thode d'Horace ???clat???e: application ??? l'interpolation en degr??? quatre, Inventiones Mathematicae, vol.403, issue.1, pp.585-602, 1992.
DOI : 10.1007/BF01231903

M. Alonso, J. Brachat, and B. Mourrain, The hilbert scheme of points and its link with border basis, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00433127

M. Barnabei, A. Brini, and G. Rota, On the exterior calculus of invariant theory, Journal of Algebra, vol.96, issue.1, pp.120-160, 1985.
DOI : 10.1016/0021-8693(85)90043-2

D. Bayer, The Division algorithm and the Hilbert Scheme, 1982.

A. Bernardi, J. Brachat, P. Comon, and B. Mourrain, Multihomogeneous polynomial decomposition using moment matrices, Proceedings of the 36th international symposium on Symbolic and algebraic computation, ISSAC '11, pp.35-42
DOI : 10.1145/1993886.1993898

URL : https://hal.archives-ouvertes.fr/inria-00638837

C. Bertone, P. Lella, and M. Roggero, Borel open covering of Hilbert schemes, 2011.

D. Bini, M. Capovani, F. Romani, and G. Lotti, O(n2.7799) complexity for n ?? n approximate matrix multiplication, Information Processing Letters, vol.8, issue.5, pp.234-235, 1979.
DOI : 10.1016/0020-0190(79)90113-3

URL : https://hal.archives-ouvertes.fr/hal-00305432

J. Brachat, P. Comon, B. Mourrain, and E. P. Tsigaridas, Symmetric tensor decomposition, Linear Algebra and its Applications, vol.433, issue.11-12, pp.11-121851, 2010.
DOI : 10.1016/j.laa.2010.06.046

URL : https://hal.archives-ouvertes.fr/inria-00355713

J. Brachat, P. Lella, M. Roggero, and B. Mourrain, Low degree equations defining the hilbert scheme, 2011.

R. Bro, PARAFAC. Tutorial and applications, Chemometrics and Intelligent Laboratory Systems, vol.38, issue.2, pp.149-171, 1997.
DOI : 10.1016/S0169-7439(97)00032-4

J. Buczynska, A. Ginensky, and J. M. Landsberg, Determinental equations for secant varieties and the Eisenbud-Koh-Stillman conjecture, 1007.

W. Buczynska and J. Buczynski, Secant varieties to high degree Veronese reembeddings, catalecticant matrices and smoothable Gorenstein schemes, Journal of Algebraic Geometry, vol.23, issue.1, 2010.
DOI : 10.1090/S1056-3911-2013-00595-0

P. Bürgisser, M. Clausen, and M. A. Shokrollahi, Algebraic complexity theory, 1997.
DOI : 10.1007/978-3-662-03338-8

J. F. Cardoso, Blind signal separation: statistical principles, Proc. of the IEEE, pp.2009-2025, 1998.
DOI : 10.1109/5.720250

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.7237

D. A. Cartwright, D. Erman, M. Velasco, and B. Viray, Hilbert schemes of 8 points, Algebra & Number Theory, vol.3, issue.7, 2008.
DOI : 10.2140/ant.2009.3.763

P. Chevalier, Optimal separation of independent narrow-band sources: Concept and performance, Signal Processing, vol.73, issue.1-2, pp.27-48, 1999.
DOI : 10.1016/S0165-1684(98)00183-2

P. Chevalier, L. Albera, A. Ferreol, and P. Comon, On the virtual array concept for higher order array processing, IEEE Transactions on Signal Processing, vol.53, issue.4, pp.1254-1271, 2005.
DOI : 10.1109/TSP.2005.843703

A. Cichocki and S. Amari, Adaptive Blind Signal and Image Processing, 2002.
DOI : 10.1002/0470845899

G. Comas and M. Seiguer, On the Rank of a Binary Form, Foundations of Computational Mathematics, vol.117, issue.2, pp.65-78, 2011.
DOI : 10.1007/s10208-010-9077-x

P. Comon, Independent Component Analysis, Higher Order Statistics, pp.29-38, 1992.
URL : https://hal.archives-ouvertes.fr/hal-00346684

P. Comon, G. Golub, L. Lim, and B. Mourrain, Symmetric Tensors and Symmetric Tensor Rank, SIAM Journal on Matrix Analysis and Applications, vol.30, issue.3, pp.1254-1279, 2008.
DOI : 10.1137/060661569

URL : https://hal.archives-ouvertes.fr/hal-00327599

P. Comon and M. Rajih, Blind identification of under-determined mixtures based on the characteristic function, Signal Processing, vol.86, issue.9, pp.2271-2281, 2006.
DOI : 10.1016/j.sigpro.2005.10.007

URL : https://hal.archives-ouvertes.fr/hal-00263668

D. Cox, J. Little, and D. Shea, Ideals, Varieties, and Algorithms. Undergraduate Texts in Mathematics, 1997.

D. Cox, J. Little, and D. Shea, Using Algebraic Geometry. Number 185 in Graduate Texts in Mathematics, 2005.
DOI : 10.1007/978-1-4757-6911-1

L. De-lathauwer and J. Castaing, Tensor-based techniques for the blind separation of DS???CDMA signals, Signal Processing, vol.87, issue.2, pp.322-336, 2007.
DOI : 10.1016/j.sigpro.2005.12.015

L. De-lathauwer, J. Castaing, and J. F. Cardoso, Fourth-Order Cumulant-Based Blind Identification of Underdetermined Mixtures, IEEE Transactions on Signal Processing, vol.55, issue.6, pp.2965-2973, 2007.
DOI : 10.1109/TSP.2007.893943

J. De-leeuw, A new computational method to fit the weighted euclidean distance model, Psychometrika, vol.22, issue.4, pp.479-490, 1978.
DOI : 10.1007/BF02293809

M. C. Dogan and J. Mendel, Applications of cumulants to array processing .I. Aperture extension and array calibration, IEEE Transactions on Signal Processing, vol.43, issue.5, pp.1200-1216, 1995.
DOI : 10.1109/78.382404

D. L. Donoho and X. Huo, Uncertainty principles and ideal atomic decomposition, IEEE Transactions on Information Theory, vol.47, issue.7, pp.2845-2862, 2001.
DOI : 10.1109/18.959265

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.161.9300

D. Eisenbud, Commutative algebra, volume 150 of Graduate Texts in Mathematics, 1995.

M. Elkadi and B. Mourrain, Introduction à la résolution des systémes polynomiaux, Mathématiques et Applications, vol.59, 2007.
DOI : 10.1007/978-3-540-71647-1

A. Ferreol and P. Chevalier, On the behavior of current second and higher order blind source separation methods for cyclostationary sources, IEEE Transactions on Signal Processing, vol.48, issue.6, pp.1712-1725990, 2000.
DOI : 10.1109/78.845929

C. Giuseppa and . Ferro, Gröbner Bases and Hilbert Schemes. I, J. Symb. Comput, vol.6, issue.23, pp.219-230, 1988.

B. N. Flury, Common Principal Components in K Groups, Journal of the American Statistical Association, vol.79, issue.388, pp.892-898, 1984.
DOI : 10.2307/2288721

G. H. Golub and C. F. Van-loan, Matrix computations, 1983.

G. Gotzmann, Eine Bedingung f???r die Flachheit und das Hilbertpolynom eines graduierten Ringes, Mathematische Zeitschrift, vol.7, issue.1, pp.61-70, 1978.
DOI : 10.1007/BF01214566

L. Mark and . Green, Generic initial ideals, Six lectures on commutative algebra, pp.119-186, 1996.

A. Grothendieck, Éléments de géométrie algébrique. I. Le langage des schémas, Inst. Hautes Études Sci. Publ. Math, issue.4, p.228, 1960.

A. Grothendieck, Éléments de géométrie algébrique. II. Étude globale élémentaire de quelques classes de morphismes, Inst. Hautes Études Sci. Publ. Math, issue.8, p.222, 1961.

A. Grothendieck, Techniques de construction et théorèmes d'existence en géométrie algébrique. IV. Les schémas de Hilbert, In Séminaire Bourbaki Exp. No, vol.6, issue.221, pp.249-276, 1961.

M. Haiman, t, q-Catalan numbers and the Hilbert scheme, Discrete Mathematics, vol.193, issue.1-3, pp.201-224, 1994.
DOI : 10.1016/S0012-365X(98)00141-1

M. Haiman and B. Sturmfels, Multigraded Hilbert schemes, Journal of Algebraic Geometry, vol.13, issue.4, pp.725-769, 2004.
DOI : 10.1090/S1056-3911-04-00373-X

J. Harris, Algebraic Geometry : A First Course. Number 133 in Graduate Texts in Mathematics, 1992.
DOI : 10.1007/978-1-4757-2189-8

R. A. Harshman and M. Lundy, PARAFAC: Parallel factor analysis, Computational Statistics & Data Analysis, vol.18, issue.1, pp.39-72, 1994.
DOI : 10.1016/0167-9473(94)90132-5

R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, vol.52, issue.52, 1977.
DOI : 10.1007/978-1-4757-3849-0

E. Mark and . Huibregtse, A description of certain affine open subschemes that form an open covering of Hilb n A 2

E. Mark and . Huibregtse, An elementary construction of the multigraded hilbert scheme of points, Pacific Journal of Mathematics, vol.223, issue.2, pp.269-315, 2006.

A. Iarrobino and V. Kanev, Power sums, Gorenstein algebras, and determinantal loci, Lecture Notes in Mathematics, vol.1721, 1999.
DOI : 10.1007/BFb0093426

A. Anthony and . Iarrobino, Reducibility of the families of 0-dimensional schemes on a variety, Invent. Math, vol.15, pp.72-77, 1972.

A. Anthony and . Iarrobino, Hilbert scheme of points : overview of last ten years, Algebraic geometry, pp.297-320, 1985.

T. Jiang and N. Sidiropoulos, Kruskal's Permutation Lemma and the Identification of CANDECOMP/PARAFAC and Bilinear Models with Constant Modulus Constraints, IEEE Transactions on Signal Processing, vol.52, issue.9, pp.2625-2636, 2004.
DOI : 10.1109/TSP.2004.832022

H. A. Kiers and W. P. Krijnen, An efficient algorithm for PARAFAC of three-way data with large numbers of observation units, Psychometrika, vol.22, issue.1, p.147, 1991.
DOI : 10.1007/BF02294592

M. Kreuzer and L. Robbiano, Deformations of border bases, Collectanea mathematica, vol.101, issue.3, pp.275-297, 2008.
DOI : 10.1007/BF03191188

J. Kung and G. Rota, The invariant theory of binary forms, Bulletin of the American Mathematical Society, vol.10, issue.1, pp.27-85, 1984.
DOI : 10.1090/S0273-0979-1984-15188-7

J. Landsberg, Geometry and the complexity of matrix multiplication, Bulletin of the American Mathematical Society, vol.45, issue.02, pp.247-284, 2008.
DOI : 10.1090/S0273-0979-08-01176-2

J. M. Landsberg and L. Manivel, On the Ideals of Secant Varieties of Segre Varieties, Foundations of Computational Mathematics, vol.4, issue.4, pp.397-422, 2004.
DOI : 10.1007/s10208-003-0115-9

J. M. Landsberg and L. Manivel, Generalizations of Strassen's Equations for Secant Varieties of Segre Varieties, Communications in Algebra, vol.384, issue.4, pp.405-422, 2008.
DOI : 10.1080/00927870701715746

J. M. Landsberg and G. Ottaviani, Equations for secant varieties of Veronese and other varieties, Annali di Matematica Pura ed Applicata, vol.52, issue.53, 2010.
DOI : 10.1007/s10231-011-0238-6

J. M. Landsberg and G. Ottaviani, Equations for secant varieties via vector bundles, 2010.
DOI : 10.1007/s10231-011-0238-6

URL : http://arxiv.org/abs/1111.4567

J. M. Landsberg and J. Weyman, On the ideals and singularities of secant varieties of Segre varieties, Bulletin of the London Mathematical Society, vol.39, issue.4, pp.685-697, 2007.
DOI : 10.1112/blms/bdm049

P. Lella and M. Roggero, Rational Components of Hilbert Schemes, Rendiconti del Seminario Matematico della Universit?? di Padova, vol.126, 2009.
DOI : 10.4171/RSMUP/126-2

URL : http://arxiv.org/abs/0903.1029

F. S. Macaulay, The Algebraic Theory of Modular Systems, 1916.

P. Mccullagh, Tensor Methods in Statistics. Monographs on Statistics and Applied Probability, 1987.

B. Mourrain, A New Criterion for Normal Form Algorithms, Lecture Notes in Comput. Sci, vol.1719, pp.430-443, 1999.
DOI : 10.1007/3-540-46796-3_41

B. Mourrain and P. Trébuchet, Stable normal forms for polynomial system solving, Theoretical Computer Science, vol.409, issue.2, pp.229-240, 2008.
DOI : 10.1016/j.tcs.2008.09.004

URL : https://hal.archives-ouvertes.fr/inria-00343103

L. Oeding and G. Ottaviani, Eigenvectors of tensors and algorithms for Waring decomposition, Journal of Symbolic Computation, vol.54, 2011.
DOI : 10.1016/j.jsc.2012.11.005

P. Paatero, The Multilinear Engine: A Table-Driven, Least Squares Program for Solving Multilinear Problems, including the n-Way Parallel Factor Analysis Model, Journal of Computational and Graphical Statistics, vol.8, issue.4, pp.854-888, 1999.
DOI : 10.2307/1390831

I. Peeva and M. Stillman, Connectedness of Hilbert schemes, Journal of Algebraic Geometry, vol.14, issue.2, pp.193-211, 2005.
DOI : 10.1090/S1056-3911-04-00386-8

D. T. Pham and J. Cardoso, Blind separation of instantaneous mixtures of nonstationary sources, IEEE Transactions on Signal Processing, vol.49, issue.9, pp.1837-1848, 2001.
DOI : 10.1109/78.942614

L. Robbiano, On border basis and groebner basis schemes, 2008.
DOI : 10.1007/bf03191213

URL : http://arxiv.org/pdf/0802.2793v1.pdf

M. Roggero, Borel open covering of hilbert schemes, 2009.

E. Sernesi, Deformations of algebraic schemes, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, vol.334, 2006.

I. R. Shafarevich, Basic algebraic geometry Schemes and complex manifolds, Translated from the, 1988.

N. D. Sidiropoulos, G. B. Giannakis, and R. Bro, Blind PARAFAC receivers for DS-CDMA systems, IEEE Transactions on Signal Processing, vol.48, issue.3, pp.810-823, 2000.
DOI : 10.1109/78.824675

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.141.1676

V. Strassen, Rank and optimal computation of generic tensors, Linear Algebra Appl, vol.52, pp.645-685, 1983.

A. Swami, G. Giannakis, and S. Shamsunder, Multichannel ARMA processes, IEEE Transactions on Signal Processing, vol.42, issue.4, pp.898-913, 1994.
DOI : 10.1109/78.285653

J. J. Sylvester, Sur une extension d'un théorème de Clebsch relatif aux courbes du quatrième degré, Comptes Rendus, Math. Acad. Sci. Paris, vol.102, pp.1532-1534, 1886.

D. Laksov, T. S. Gustavsen, and R. M. Skjelnes, An elementary, explicit, proof of the existence of the hilbert scheme of points, p.506161, 2005.

J. M. Ten-berge, N. D. Sidiropoulos, and R. Rocci, Typical rank and indscal dimensionality for symmetric three-way arrays of order I??2??2 or I??3??3, Linear Algebra and its Applications, vol.388, pp.363-377, 2004.
DOI : 10.1016/j.laa.2004.03.009

K. Ueno, Algebraic geometry. 3, volume 218 of Translations of Mathematical Monographs Further study of schemes, Translated from the, Japanese original by Goro Kato, Iwanami Series in Modern Mathematics, 1998.

A. J. Van-der-veen and A. Paulraj, An analytical constant modulus algorithm, IEEE Transactions on Signal Processing, vol.44, issue.5, pp.1136-1155, 1996.
DOI : 10.1109/78.502327

A. Yeredor, Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation, IEEE Transactions on Signal Processing, vol.50, issue.7, pp.1545-1553, 2002.
DOI : 10.1109/TSP.2002.1011195

F. L. Zak, Tangents and secants of algebraic varieties, Translations of Mathematical Monographs. AMS, vol.127, 1993.

A. Ziehe, G. Nolte, and K. R. Müller, A fast algorithm for joint diagonalization with non orthogonal transformations and its application to blind source separation, Journal of Machine Learning Research, vol.5, pp.777-800, 2004.