On mixed discriminants of positively definite matrix
نویسندگان
چکیده
منابع مشابه
Mixed Discriminants
The mixed discriminant of n Laurent polynomials in n variables is the irreducible polynomial in the coefficients which vanishes whenever two of the roots coincide. The Cayley trick expresses the mixed discriminant as an A-discriminant. We show that the degree of the mixed discriminant is a piecewise linear function in the Plücker coordinates of a mixed Grassmannian. An explicit degree formula i...
متن کاملComputing Mixed Discriminants , Mixed Volumes
We construct a probabilistic polynomial time algorithm that computes the mixed discriminant of given n positive definite n × n matrices within a 2O(n) factor. As a corollary, we show that the permanent of an n×n nonnegative matrix and the mixed volume of n ellipsoids inRn can be computed within a 2O(n) factor by probabilistic polynomial time algorithms. Since every convex body can be approximat...
متن کاملPlane mixed discriminants and toric jacobians
Polynomial algebra offers a standard approach to handle several problems in geometric modeling. A key tool is the discriminant of a univariate polynomial, or of a well-constrained system of polynomial equations, which expresses the existence of a multiple root. We describe discriminants in a general context, and focus on exploiting the sparseness of polynomials via the theory of Newton polytope...
متن کاملOn the Effective Permeability of Mixed Matrix Membranes
Mixed matrix membranes (MMMs) are attracting significant interest for pervaporation and gas separation applications. To better comprehend the impact of filler particles within polymer matrices, the species permeation mass transport was theoretically studied by numerical simulation using finite differences. The Fick’s second law of diffusion was solved for a three-dimensional MMM to obtain the c...
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: Ars Mathematica Contemporanea
سال: 2015
ISSN: 1855-3974,1855-3966
DOI: 10.26493/1855-3974.403.423