Computing symmetric rank for symmetric tensors
Tài liệu tham khảo
Albera, 2005, On the virtual array concept for higher order array processing, IEEE Trans. Signal Process., 53, 1254, 10.1109/TSP.2005.843703
Alexander, 1995, Polynomial interpolation in several variables, J. Algebraic Geom., 4, 201
Arrondo, Enrique, Bernardi, Alessandra, 2009. On the variety parametrizing completely decomposable polynomials. Preprint, http://arxiv.org/abs/0903.2757.
Arrondo, 2005, Characterization of Veronese varieties via projections in Grassmannians, 1
Bernardi, 2007, Osculating varieties of Veronesean and their higher secant varieties, Canad. J. Math., 59, 488, 10.4153/CJM-2007-021-6
Brachat, Jerome, Comon, Pierre, Mourrain, Bernard, Tsigaridas, Elias P., 2009. Symmetric tensors decomposition. Preprint, http://arxiv.org/abs/0901.3706.
Brambilla, 2008, On the Alexander–Hirschowitz theorem, J. Pure Appl. Algebra, 212, 1229, 10.1016/j.jpaa.2007.09.014
Carlini, 2005, Reducing the number of variables of a polynomial, 237
Catalisano, 2008, On the ideals of Secant Varieties to certain rational varieties, J. Algebra, 319, 1913, 10.1016/j.jalgebra.2007.01.045
Chevalier, 1999, Optimal separation of independent narrow-band sources - concept and performance, Signal Process., 73, 27, 10.1016/S0165-1684(98)00183-2
CoCoA Team, 2009. CoCoA: A system for doing computations in commutative algebra. Available at http://cocoa.dima.unige.it.
Comon, 1992, Independent component analysis, 29
Comon, 2002, Tensor decompositions, 1
Comon, 2006, Blind identification of under-determined mixtures based on the characteristic function, Signal Process., 86, 2271, 10.1016/j.sigpro.2005.10.007
Comas, Gonzalo, Seiguer, Malena, 2001. On the rank of a binary form. Preprint, http://arxiv.org/abs/math/0112311.
De Lathauwer, 2007, Tensor-based techniques for the blind separation of ds-cdma signals, Signal Process., 87, 322, 10.1016/j.sigpro.2005.12.015
De Lathauwer, 2000, A multilinear singular value decomposiotion, SIAM J. Matrix Anal. Appl., 21, 1253, 10.1137/S0895479896305696
Dogaˇn, 1995, Applications of cumulants to array processing. I. aperture extension and array calibration, IEEE Trans. Signal Process., 43, 1200, 10.1109/78.382404
Geramita, 1999, Catalecticant varieties, vol. 206, 143
Gherardelli, 1996, Osservazioni su una classe di Varietá determinantali, Rend. Istituto Lombardo A, 130, 163
Golub, 1983
Iarrobino, 1999, Power sums, Gorenstein algebras, and determinantal loci, vol. 1721
Jiang, 2004, Kruskals permutation lemma and the identification of CANDECOMP/PARAFAC and bilinear models, IEEE Trans. Signal Process., 52, 2625, 10.1109/TSP.2004.832022
Kanev, 1999, Chordal varieties of Veronese varieties and catalecticant matrices, J. Math. Sci. (New York), 94, 1114, 10.1007/BF02367252
Landsberg, Joseph M., Ottaviani, Giorgio, 2010. Equations for secant varieties of Veronese varieties. Preprint,http://arXiv.org/abs/1006.0180.
Landsberg, 2010, On the ranks and border ranks of symmetric tensors, Found. Comput. Math., 10, 339, 10.1007/s10208-009-9055-3
Lim, 2008, Tensor rank and ill-posedness of the best low-rank approssimation problem, SIAM J. Matrix Anal. Appl., 31, 1084
McCullagh, 1987, Tensor methods in statistics
Murnaghan, 1938
Oldenburger, 1934, Composition and rank of n-way matrices and multilinear forms, Ann. Math., 35, 622, 10.2307/1968754
Ottaviani, 2009, An invariant regarding warings problem for cubic polynomials, Nagoya Math. J., 193, 95, 10.1017/S0027763000026040
Piene, 1981, Cuspidal projections of space curves, Math. Ann., 256, 95, 10.1007/BF01450947
Sidiropoulos, 2000, Parallel factor analysis in sensor array processing, IEEE Trans. Signal Process., 48, 2377, 10.1109/78.852018
Sylvester, 1886, Sur une extension d’un théorème de Clebsh relatif aux courbes du quatrième degré, Comptes Rendus, Math. Acad. Sci. Paris, 102, 1532
Waring, 1991, Meditationes Algebricae, 1770, Cambridge: J. Archdeacon.