A. Anandkumar, D. P. Foster, D. J. Hsu, and M. Sham,

Y. Kakade and . Liu, A spectral algorithm for latent dirichlet allocation, Advances in Neural Information Processing Systems, pp.917-925, 2012.

R. Agh-+-15]-anima-anandkumar, D. Ge, . Hsu, M. Sham, M. Kakade et al., Tensor decompositions for learning latent variable models (A survey for ALT), International Conference on Algorithmic Learning Theory, pp.19-38, 2015.

A. Anandkumar, D. Hsu, and S. M. Kakade, A method of moments for mixture models and hidden Markov models, Conference on Learning Theory, pp.33-34, 2012.

T. Austin, On exchangeable random variables and the statistics of large graphs and hypergraphs. Probability Surveys, vol.5, pp.80-145, 2008.

A. Bernardi, J. Brachat, P. Comon, and B. Mourrain, General tensor decomposition, moment matrices and applications, Journal of Symbolic Computation, vol.52, pp.51-71, 2013.
URL : https://hal.archives-ouvertes.fr/inria-00590965

M. Briani, A. Cuyt, and W. Lee, , 2017.

A. Bernardi, N. S. Daleo, J. D. Hauenstein, and B. Mourrain, Tensor decomposition and homotopy 148 continuation. Differential Geometry and its Applications, vol.55, pp.78-105, 2017.

A. Bernardi, Ideals of varieties parameterized by certain symmetric tensors, Journal of Pure and Applied Algebra, vol.212, issue.6, pp.1542-1559, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00645965

J. Peter, J. Basser, D. Mattiello, and . Lebihan, Estimation of the effective self-diffusion tensor from the NMR spin echo, Journal of Magnetic Resonance, Series B, vol.103, issue.3, pp.247-254, 1994.

D. Bini, Y. Victor, and . Pan, Polynomial and Matrix Computations: Fundamental Algorithms, 2012.

R. Bro and . Parafac, Tutorial and applications. Chemometrics and intelligent laboratory systems, vol.38, pp.149-171, 1997.

S. Boyd and L. Vandenberghe, Convex Optimization, 2004.

J. Cai, E. J. Candès, and Z. Shen, A singular value thresholding algorithm for matrix completion, SIAM Journal on Optimization, vol.20, issue.4, pp.1956-1982, 2010.

A. R. Conn, N. I. Gould, and P. L. Toint, An introduction to the structure of large scale nonlinear optimization problems and the LANCELOT project, Computing Methods in Applied Sciences and Engineering, pp.42-54, 1990.

A. Cuyt and W. Lee, Multivariate exponential analysis from the minimal number of samples, Advances in Computational Mathematics, vol.44, issue.4, pp.987-1002, 2018.

E. J. Candès and B. Recht, Exact matrix completion via convex optimization, Foundations of Computational mathematics, vol.9, issue.6, p.149, 2009.

E. J. Candès and T. Tao, The power of convex relaxation: Near-optimal matrix completion, IEEE Transactions on Information Theory, vol.56, issue.5, pp.2053-2080, 2010.

A. Cuyt, M. Tsai, M. Verhoye, and W. Lee, Faint and clustered components in exponential analysis, Applied Mathematics and Computation, vol.327, pp.93-103, 2018.

. Lieven-de-lathauwer, Signal Processing Based on Multilinear Algebra, 1997.

J. Lieven-de-lathauwer and . Castaing, Tensor-based techniques for the blind separation of DS-CDMA signals, Signal Processing, vol.87, issue.2, pp.322-336, 2007.

B. D. Lieven-de-lathauwer, J. Moor, and . Vandewalle, Computation of the canonical decomposition by means of a simultaneous generalized Schur decomposition, SIAM journal on Matrix Analysis and Applications, vol.26, issue.2, pp.295-327, 2004.

M. Elkadi and B. Mourrain, IntroductionàIntroductionà La Résolution Des Systèmes Polynomiaux, vol.59, 2007.

J. Emsalem, Géométrie des pointsépaispointsépais, Bull. Soc. Math. France, vol.106, issue.4, pp.399-416, 1978.

M. Fazel, Matrix Rank Minimization with Applications, 2002.

A. Ghosh, R. Deriche, and M. Moakher, Ternary quartic approach for positive 4th order diffusion tensors revisited, Biomedical Imaging: From Nano to Macro, 2009. ISBI'09. IEEE International Symposium On, pp.618-621, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00496873

G. H. Golub, CF Van loan, Matrix computations. The Johns Hopkins, 1996.

T. Huy, Box-shaped matrices and the defining ideal of certain blowup surfaces, Journal of Pure and Applied Algebra, vol.167, issue.2-3, pp.203-224, 2002.

F. Huang and A. Anandkumar, Convolutional dictionary learning through tensor factorization, Feature Extraction: Modern Questions and Challenges, pp.116-129, 2015.

D. Hsu, M. Sham, and . Kakade, Learning mixtures of spherical gaussians: Moment methods and spectral decompositions, Proceedings of the 4th Conference on Innovations in Theoretical Computer Science, pp.11-20, 2013.

J. Harmouch, H. Khalil, and B. Mourrain, Structured low rank decomposition of multivariate Hankel matrices, Linear Algebra and its Applications, vol.542, pp.162-185, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01440063

J. Harmouch, B. Mourrain, and H. Khalil, Decomposition of Low Rank Multi-Symmetric Tensor, International Conference on Mathematical Aspects of Computer and Information Sciences, pp.51-66, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01648747

S. Hosseini, On the Convex Geometry of Weighted Nuclear Norm Minimization, 2016.

A. Hakop, M. G. Hakopian, and . Tonoyan, Partial differential analogs of ordinary differential equations and systems, New York J. Math, vol.10, pp.89-116, 2004.

F. Jiao, Y. Gur, C. R. Johnson, and S. Joshi, Detection of crossing white matter fibers with high-order tensors and rank-k decompositions, Biennial International Conference on Information Processing in Medical Imaging, pp.538-549, 2011.

T. Kolda and B. Bader, Tensor Decompositions and Applications, SIAM Review, vol.51, issue.3, pp.455-500, 2009.

S. Kruk, M. Muramatsu, F. Rendl, R. J. Vanderbei, and H. Wolkowicz, The Gauss-Newton direction in semidefinite programming, Optimization Methods and Software, vol.15, issue.1, pp.1-28, 2001.

S. Kunis, T. Peter, T. Römer, and U. Von-der-ohe, A multivariate generalization of Prony's method, Linear Algebra and its Applications, vol.490, pp.31-47, 2016.

L. Kronecker, Zur Theorie Der Elimination Einer Variabeln Aus Zwei Algebraischen Gleichungen von L. Kronecker

G. Vogt, , p.1881

,. D. John-little, D. Cox, and . O'shea, Ideals, varieties, and algorithms, Contemporary Mathematics, issue.133, 1992.

L. Lim, Singular values and eigenvalues of tensors: A variational approach, 1st IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, pp.129-132, 2005.

T. Megherbi, M. Kachouane, F. O. Boumghar, and R. Deriche, Détection des croisements de fibre en IRM de diffusion par décomposition de tenseur: Approche analytique, Reconnaissance de Formes et Intelligence Artificielle (RFIA), 2014.

B. Mourrain, Isolated points, duality and residues, Journal of Pure and Applied Algebra, vol.117, pp.469-493, 1997.
URL : https://hal.archives-ouvertes.fr/inria-00125278

B. Mourrain, Polynomial-Exponential Decomposition From Moments, Foundations of Computational Mathematics, pp.1-58, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01367730

J. Nocedal and S. J. Wright, Springer Series in Operations Research. Numerical Optimization, p.152, 1999.

U. Oberst and F. Pauer, The constructive solution of linear systems of partial difference and differential equations with constant coefficients, Multidimensional Systems and Signal Processing, vol.12, issue.3-4, pp.253-308, 2001.

Y. Victor and . Pan, How bad are Vandermonde matrices?, SIAM Journal on Matrix Analysis and Applications, vol.37, issue.2, pp.676-694, 2016.

P. S. Pedersen, Basis for power series solutions to systems of linear, constant coefficient partial differential equations, Advances in Mathematics, vol.141, issue.1, pp.155-166, 1999.

V. Pereyra and G. Scherer, Exponential Data Fitting and Its Applications, 2010.

D. Potts and M. Tasche, Parameter estimation for multivariate exponential sums, Electronic Transactions on Numerical Analysis, vol.40, pp.204-224, 2013.

G. Plonka and M. Tasche, Prony methods for recovery of structured functions, vol.37, pp.239-258, 2014.

M. Pucci, The Veronese variety and catalecticant matrices, Journal of Algebra, vol.202, issue.1, pp.72-95, 1998.

L. Qi, Eigenvalues of a real supersymmetric tensor, Journal of Symbolic Computation, vol.40, issue.6, pp.1302-1324, 2005.

B. Recht, M. Fazel, and P. A. Parrilo, Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization, SIAM review, vol.52, issue.3, pp.471-501, 2010.

H. Richard, T. Roy, and . Kailath, ESPRIT-Estimation of signal parameters via rotational invariance techniques, Optical Engineering, vol.29, issue.4, pp.296-314, 1990.

T. Sauer, Prony's method in several variables, Numerische Mathematik, vol.136, issue.2, p.153, 2017.

T. Sauer, Prony's method in several variables: Symbolic solutions by universal interpolation, Journal of Symbolic Computation, vol.84, pp.95-112, 2018.

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.

E. Sanchez and B. R. Kowalski, Tensorial resolution: A direct trilinear decomposition, Journal of Chemometrics, vol.4, issue.1, pp.29-45, 1990.

A. , L. Swindlehurst, and T. Kailath, A performance analysis of subspace-based methods in the presence of model errors, Part I: The MUSIC algorithm, IEEE Trans. Signal Processing, vol.40, issue.7, pp.1758-1774, 1992.

A. Stegeman, On uniqueness of the n th order tensor decomposition into rank-1 terms with linear independence in one mode, SIAM Journal on Matrix Analysis and Applications, vol.31, issue.5, pp.2498-2516, 2010.

A. Stegeman, On uniqueness of the canonical tensor decomposition with some form of symmetry, SIAM Journal on Matrix Analysis and Applications, vol.32, issue.2, pp.561-583, 2011.

J. Tournier, F. Calamante, and A. Connelly, Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution, Neuroimage, vol.35, issue.4, pp.1459-1472, 2007.

M. J. Todd, A study of search directions in primal-dual interior-point methods for semidefinite programming, 1997.

K. Usevich and P. Comon, Quasi-Hankel lowrank matrix completion: A convex relaxation, p.154, 2015.

L. Vandenberghe and S. Boyd, Semidefinite programming, SIAM review, vol.38, pp.49-95, 1996.

T. Yonas, A. Weldeselassie, M. S. Barmpoutis, and . Atkins, Symmetric positive semi-definite cartesian tensor fiber orientation distributions (CT-FOD), Medical Image Analysis, vol.16, issue.6, pp.1121-1129, 2012.

Y. Xu and W. Yin, A block coordinate descent method for regularized multiconvex optimization with applications to nonnegative tensor factorization and completion, SIAM Journal on imaging sciences, vol.6, issue.3, pp.1758-1789, 2013.

A. Ziehe, P. Laskov, G. Nolte, and K. A?ller, A fast algorithm for joint diagonalization with nonorthogonal transformations and its application to blind source separation, Journal of Machine Learning Research, vol.5, pp.777-800, 2004.