Effective identifiability criteria for tensors and polynomials
نویسندگان
چکیده
منابع مشابه
Effective identifiability criteria for tensors and polynomials
A tensor T , in a given tensor space, is said to be h-identifiable if it admits a unique decomposition as a sum of h rank one tensors. A criterion for h-identifiability is called effective if it is satisfied in a dense, open subset of the set of rank h tensors. In this paper we give effective h-identifiability criteria for a large class of tensors. We then improve these criteria for some symmet...
متن کاملIdentifiability beyond Kruskal’s Bound for Symmetric Tensors of Degree 4
We show how methods of algebraic geometry can produce criteria for the identifiability of specific tensors that reach beyond the range of applicability of the celebrated Kruskal criterion. More specifically, we deal with the symmetric identifiability of symmetric tensors in Sym4(Cn+1), i.e., quartic hypersurfaces in a projective space Pn, that have a decomposition in 2n + 1 summands of rank 1. ...
متن کاملExact relations for effective tensors of polycrystals. I: Necessary conditions
The set of all effective moduli of a polycrystal usually has a nonempty interior. When it does not, we say that there is an exact relation for effective moduli. This can indeed happen as evidenced by recent results [4, 10, 12] on polycrystals. In this paper we describe a general method for finding such relations for effective moduli of laminates. The method is applicable to any physical setting...
متن کاملGauge Invariant Effective Stress-energy Tensors for Gravitational Waves
It is shown that if a generalized definition of gauge invariance is used, gauge invariant effective stress-energy tensors for gravitational waves and other gravitational perturbations can be defined in a much larger variety of circumstances than has previously been possible. In particular it is no longer necessary to average the stress-energy tensor over a region of spacetime which is larger in...
متن کاملAn Effective Lojasiewicz Inequality for Real Polynomials
Example 1. Set f1 = x d 1 and fi = xi−1 − x d i for i = 2, . . . , n. Then Φ(x) := maxi{|fi(x)|} > 0 for x 6= 0. Let p(t) = (t d , t n−2 , . . . , t). Then limt→0 ||p(t)||/|t| = 1 and Φ(p(t)) = t d . Thus the Lojasiewicz exponent is ≥ d. (In fact it equals d.) This works both over R and C. In the real case set F = ∑ f 2 i . Then degF = 2d, F has an isolated real zero at the origin and the Lojas...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2018
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2017.11.006