Waring, tangential and cactus decompositions
نویسندگان
چکیده
منابع مشابه
Waring Decompositions of Monomials
A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of linear forms, where the number of summands is minimal possible. We prove that any Waring decomposition of a monomial is obtained from a complete intersection ideal, determine the dimension of the set of Waring decompositions, and give the conditions under which the Waring decomposition is unique up t...
متن کاملTangential frequency ltering decompositions
In this paper, new robust algorithms for the solution of systems of linear equations which arise from the discretisation of partial diierential equations with strongly varying coeecients are introduced. These iterative methods are based on the tangential frequency ltering decompositions. The existence of the TFFD and the convergence of the induced iterative algorithms is shown for symmetric and...
متن کاملTangential Frequency Ltering Decompositions for Symmetric Matrices
The tangential frequency ltering decomposition (TFFD) is introduced. The convergence theory of an iterative scheme based on the TFFD for symmetric matrices is the focus of this paper. The existence of the TFFD and the convergence of the induced iterative algorithm is shown for symmetric and positive deenite matrices. Convergence rates independent of the number of unknowns are proven for a small...
متن کاملEla a Remark on Waring Decompositions of Some Special Plane Quartics∗
Motivated by questions on tensor rank, this work concerns the following unexpected result concerning Waring decompositions of plane quartics containing a double line, along with some preparatory and additional remarks. Let x, l1, . . . , l7 be linear forms and q a quadratic form on a vector space of dimension 3. If xq = l 1 + · · · + l 7 and the lines l1 = 0, . . ., l7 = 0 in P intersect x = 0 ...
متن کاملFrom Fermat to Waring
The ring Zk(+, .) mod p k with prime power modulus (prime p > 2) is analysed. Its cyclic group Gk of units has order (p − 1)p, and all p-th power n residues form a subgroup Fk with |Fk| = |Gk|/p. The subgroup of order p − 1, the core Ak of Gk, extends Fermat’s Small Theorem (FST ) to mod p, consisting of p − 1 residues with n ≡ n mod p. The concept of carry, e.g. n in FST extension n ≡ np + 1 m...
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 de Mathématiques Pures et Appliquées
سال: 2020
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2020.07.003