EuDML | Browse

Page 1

Displaying 1 – 12 of 12

A fast numerical test of multivariate polynomial positiveness with applications

Petr Augusta, Petra Augustová (2018)

Kybernetika

The paper presents a simple method to check a positiveness of symmetric multivariate polynomials on the unit multi-circle. The method is based on the sampling polynomials using the fast Fourier transform. The algorithm is described and its possible applications are proposed. One of the aims of the paper is to show that presented algorithm is significantly faster than commonly used method based on the semi-definite programming expression.

A generalization of the Gauss-Lucas theorem

J. L. Díaz-Barrero, J. J. Egozcue (2008)

Czechoslovak Mathematical Journal

Given a set of points in the complex plane, an incomplete polynomial is defined as the one which has these points as zeros except one of them. The classical result known as Gauss-Lucas theorem on the location of zeros of polynomials and their derivatives is extended to convex linear combinations of incomplete polynomials. An integral representation of convex linear combinations of incomplete polynomials is also given.

In the paper an elementary and simple proof of the Fundamental Theorem of Algebra is given.

Displaying 1 – 12 of 12

A fast numerical test of multivariate polynomial positiveness with applications

A generalization of the Gauss-Lucas theorem

A geometric maximization problem

A note on Robinson's non-negativity criterion

A remark on the Chebotarev theorem about roots of unity.

A Remark on the Multidimensional Moment Problem.

A simple counterexample to Kouchnirenko's conjecture.

A simple proof of the Fundamental Theorem of Algebra

Algebraic numbers near the unit circle

An application of the Gelfand-Mazur theorem: the fundamental theorem of algebra revisited.

Asymptotic behavior for the best lower bound of Jensen's functional

Auxiliary polynomials for some problems regarding Mahler's measure

Currently displaying 1 – 12 of 12