منابع مشابه
Arithmetic Circuits and the Hadamard Product of Polynomials
Motivated by the Hadamard product of matrices we define the Hadamard product of multivariate polynomials and study its arithmetic circuit and branching program complexity. We also give applications and connections to polynomial identity testing. Our main results are the following. • We show that noncommutative polynomial identity testing for algebraic branching programs over rationals is comple...
متن کاملHadamard Product of Simple Sets of Polynomials in Cn
In this paper we give some convergence properties of Hadamard product set of polynomials defined by several simple monic sets of several complex variables in complete Reinhardt domains and in hyperelliptical regions too.
متن کاملProduct of Four Hadamard Matrices
We prove that if there exist Hadamard matrices of order 4m, 4n, 4p, and 4q then there exists an Hadamard matrix of order 16mnpq. This improves and extends the known result of Agayan that there exists a Hadamard matrix of order 8mn if there exist Hadamard matrices of order 4m and 4n. Disciplines Physical Sciences and Mathematics Publication Details R. Craigen, Jennifer Seberry and Xian-Mo Zhang,...
متن کاملThe Product of Four Hadamard Matrices
We prove that if there exist Hadamard matrices of order 4m, 4n, 4p, 4q then there exists an Hadamard matrix of order 16mnpq. This improves and extends the known result of Agayan that there exists an Hadamard matrix of order 8mn if there exist Hadamard matrices of order 4m and 4n.
متن کاملHadamard Factorization of Hurwitz Stable Polynomials
The Hurwitz stable polynomials are important in the study of differential equations systems and control theory (see [7] and [19]). A property of these polynomials is related to Hadamard product. Consider two polynomials p, q ∈ R[x]: p(x) = anx n + an−1x n−1 + · · ·+ a1x + a0 q(x) = bmx m + bm−1x m−1 + · · ·+ b1x + b0 the Hadamard product (p ∗ q) is defined as (p ∗ q)(x) = akbkx + ak−1bk−1x + · ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2015
ISSN: 0021-9045
DOI: 10.1016/j.jat.2015.01.002