A. A. Gillette, A. Rand, and C. Bajaj, Error estimates for generalized barycentric interpolation, Advances in Computational Mathematics, vol.72, issue.1, pp.417-439, 2012.
DOI : 10.1007/s10444-011-9218-z

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549276

C. Abrams and G. Bussi, Enhanced Sampling in Molecular Dynamics Using Metadynamics, Replica-Exchange, and Temperature-Acceleration, Entropy, vol.16, issue.1, pp.163-199, 2014.
DOI : 10.3390/e16010163

C. Bajaj, B. Bauer, R. Bettadapura, and A. Vollrath, Nonuniform Fourier Transforms for Rigid-Body and Multidimensional Rotational Correlations, SIAM Journal on Scientific Computing, vol.35, issue.4, pp.821-845, 2013.
DOI : 10.1137/120892386

C. Bayer and J. Teichmann, The proof of Tchakaloff's Theorem, Proc. Amer, pp.3035-3040, 2006.

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.
DOI : 10.1016/j.jsc.2012.05.012

URL : https://hal.archives-ouvertes.fr/inria-00590965

J. Brachat, P. Comon, B. Mourrain, and E. Tsigaridas, Symmetric tensor decomposition . Linear Algebra and Applications, pp.1851-1872, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00355713

T. N. Patterson and C. R. Morrow, Construction of algebraic cubature rules using polynomial ideal theory, SIAM J. Numer. Anal, vol.15, pp.953-976, 1978.

R. Caflisch, W. Morokoff, and A. Owen, Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension, The Journal of Computational Finance, vol.1, issue.1, pp.27-46, 1997.
DOI : 10.21314/JCF.1997.005

R. Cools, Constructing cubature formulae: the science behind the art, Acta Numerica, vol.3, pp.1-54, 1997.
DOI : 10.1007/BF02165125

D. Cox, Solving equations via algebras, Solving Polynomial Equations: Foundations, Algorithms, and Applications, pp.63-123, 2005.
DOI : 10.1007/3-540-27357-3_2

R. E. Curto and L. A. Fialkow, Recursiveness, positivity, and truncated moment problems, Houston J. Math, vol.17, issue.4, pp.603-635, 1991.

R. E. Curto and L. Fialkow, Flat extensions of positive moment matrices: recursively generated relations, Memoirs of the American Mathematical Society, vol.136, issue.648, pp.1-64, 1998.
DOI : 10.1090/memo/0648

R. E. Curto and L. Fialkow, The truncated complex k-moment problem. Transactions of the, pp.2825-2855, 2000.

D. Eisenbud, Commutative Algebra with a view toward Algebraic Geometry, Graduate Texts in Math, vol.150, 1994.

M. Elkadi and B. Mourrain, Introduction à la résolution des systèmes d'équations algébriques, of Mathématiques et Applications, 2007.

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

A. Gillette and C. Bajaj, Dual formulations of mixed finite element methods with applications, Computer-Aided Design, vol.43, issue.10, pp.1213-1221, 2011.
DOI : 10.1016/j.cad.2011.06.017

I. S. Iohvidov, Hankel and toeplitz matrices and forms. . birkhauser. Algebraic theory. Translated from the Russian by G. Philip A. Thijsse. With an introduction by I. Gohberg, 1982.

J. Lasserre, Moments, positive polynomials and their applications, 2009.
DOI : 10.1142/p665

J. B. Lasserre, M. Laurent, B. Mourrain, P. Rostalski, and P. Trébuchet, Moment matrices, border bases and real radical computation, Journal of Symbolic Computation, vol.51, 2012.
DOI : 10.1016/j.jsc.2012.03.007

URL : https://hal.archives-ouvertes.fr/hal-00651759

M. Laurent, Revisiting two theorems of Curto and Fialkow on moment matrices, Proc. Amer. Math. Soc, pp.2965-2976, 2005.

M. Laurent, Sums of Squares, Moment Matrices and Optimization Over Polynomials, IMA volume Emerging Applications of Algebraic Geometry. IMA, 2008.
DOI : 10.1007/978-0-387-09686-5_7

M. Laurent, Sums of Squares, Moment Matrices and Optimization Over Polynomials, Mathematics and its Applications, pp.157-270, 2009.
DOI : 10.1007/978-0-387-09686-5_7

M. Laurent and B. Mourrain, A generalized flat extension theorem for moment matrices, Archiv der Mathematik, vol.38, issue.1, pp.87-98, 2009.
DOI : 10.1007/s00013-009-0007-6

H. M. Möller, Minimum-point cubature formulas, Numerische Mathematik, vol.52, issue.No. 3, pp.185-20076, 1975.
DOI : 10.1007/BF01462272

H. M. Möller, Lower Bounds for the Number of Nodes in Cubature Formulae, Numerische Integration of International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D'Analyse Numérique, pp.221-230, 1979.
DOI : 10.1007/978-3-0348-6288-2_17

H. M. Möller, Lower Bounds for the Number of Nodes in Cubature Formulae, Internat. Ser. Numer. Math, vol.45, pp.221-230, 1979.
DOI : 10.1007/978-3-0348-6288-2_17

B. Mourrain, A New Criterion for Normal Form Algorithms, AAECC, pp.430-443, 1999.
DOI : 10.1007/3-540-46796-3_41

B. Mourrain and P. Trébuchet, Generalized normal forms and polynomial system solving, Proceedings of the 2005 international symposium on Symbolic and algebraic computation , ISSAC '05, pp.253-260, 2005.
DOI : 10.1145/1073884.1073920

URL : https://hal.archives-ouvertes.fr/inria-00070537

I. P. Mysovskikh, Proof of the minimality of the number of nodes in the cubature formula for a hypersphere, USSR Computational Mathematics and Mathematical Physics, vol.6, issue.4, pp.621-630, 1966.
DOI : 10.1016/0041-5553(66)90002-4

I. P. Mysovskikh, Interpolational cubature formulas (russian), pp.1-336, 1981.

Y. Nesterov and A. Nemirovski, Interior-point polynomial algorithms in convex programming, 1994.
DOI : 10.1137/1.9781611970791

S. Ninomiya and S. Tezuka, Toward real-time pricing of complex financial derivatives, Applied Mathematical Finance, vol.41, issue.1, pp.1-20, 1996.
DOI : 10.1016/0304-405X(77)90016-2

M. Putinar, A Dilation Theory Approach to Cubature Formulas. II, Mathematische Nachrichten, vol.211, issue.1, pp.183-192, 1997.
DOI : 10.1002/(SICI)1522-2616(200003)211:1<159::AID-MANA159>3.0.CO;2-R

J. Radon, Zur mechanischen kubatur. (German) Monatsh, Math, vol.52, pp.286-300, 1948.
DOI : 10.1007/bf01525334

A. Rand, A. Gillette, and C. Bajaj, Interpolation error estimates for mean value coordinates over convex polygons, Advances in Computational Mathematics, vol.26, issue.3, pp.327-347, 2013.
DOI : 10.1007/s10444-012-9282-z

A. Rand, A. Gillette, and C. Bajaj, Quadratic serendipity finite elements on polygons using generalized barycentric coordinates, Mathematics of Computation, vol.83, issue.290, pp.2691-2716, 2014.
DOI : 10.1090/S0025-5718-2014-02807-X

B. Recht, M. Fazel, and P. Parrilo, Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization, SIAM Review, vol.52, issue.3, pp.471-501, 2010.
DOI : 10.1137/070697835

H. J. Schmid, Two-Dimensional Minimal Cubature Formulas and Matrix Equations, SIAM Journal on Matrix Analysis and Applications, vol.16, issue.3, pp.898-921, 1995.
DOI : 10.1137/S0895479893252404

H. J. Schmid and Y. Xu, On bivariate Gaussian cubature formulae, Proc. Amer, pp.833-841, 1994.
DOI : 10.1090/S0002-9939-1994-1209428-0

A. H. Stroud, QUADRATURE METHODS FOR FUNCTIONS OF MORE THAN ONE VARIABLE, Annals of the New York Academy of Sciences, vol.6, issue.2, pp.776-791, 1960.
DOI : 10.1111/j.1749-6632.1960.tb42842.x

A. H. Stroud, Integration Formulas and Orthogonal Polynomials, SIAM Journal on Numerical Analysis, vol.4, issue.3, pp.271-276, 1970.
DOI : 10.1137/0704034

V. Tchakaloff, Formules de cubatures mécaniques à coefficients non négatifs, Bull. Sci. Math, vol.81, issue.2, pp.123-134, 1957.

E. Wachpress, A rational finite element basis, 1975.

Y. Xu, Common zeros of polynomials in several variables and higherdimensional quadrature, Pitman Research Notes in Mathematics Series, vol.312, issue.312, p.119, 1994.

Y. Xu, Cubature Formulae and Polynomial Ideals, Advances in Applied Mathematics, vol.23, issue.3, pp.211-233, 1999.
DOI : 10.1006/aama.1999.0652

URL : http://doi.org/10.1006/aama.1999.0652

M. Bucero, B. Antipolis, C. France, and . Bajaj, Mourrain: Inria Sophia Antipolis Méditerranée, pp.78712-78739, 2004.