Lower bounds for univariate polynomials : a Wronskian approach
نویسندگان
چکیده
This is the nal report of an internship in algebraic complexity. First, we give an introduction to algebraic complexity and we give some motivations for the study of the main model. Then we present two di erent tools we studied during this internship and use them to establish some lower bounds on this model. We nally discuss whether those bounds could be improved or not.
منابع مشابه
Lower Bounds by Birkhoff Interpolation
In this paper we give lower bounds for the representation of real univariate polynomials as sums of powers of degree 1 polynomials. We present two families of polynomials of degree d such that the number of powers that are required in such a representation must be at least of order d. This is clearly optimal up to a constant factor. Previous lower bounds for this problem were only of order Ω( √...
متن کاملA Wronskian Approach to the real τ-conjecture
According to the real τ -conjecture, the number of real roots of a sum of products of sparse univariate polynomials should be polynomially bounded in the size of such an expression. It is known that this conjecture implies a superpolynomial lower bound on the arithmetic circuit complexity of the permanent. In this paper, we use the Wronksian determinant to give an upper bound on the number of r...
متن کاملA Wronskian Approach to the real \tau-conjecture
According to the real τ -conjecture, the number of real roots of a sum of products of sparse univariate polynomials should be polynomially bounded in the size of such an expression. It is known that this conjecture implies a superpolynomial lower bound on the arithmetic circuit complexity of the permanent. In this paper, we use the Wronksian determinant to give an upper bound on the number of r...
متن کاملLower Bounds for Sums of Powers of Low Degree Univariates
We consider the problem of representing a univariate polynomial f(x) as a sum of powers of low degree polynomials. We prove a lower bound of Ω (√ d t ) for writing an explicit univariate degree-d polynomial f(x) as a sum of powers of degree-t polynomials.
متن کاملOn Bounds For The Zeros of Univariate Polynomials
Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated. Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we deal with the location of zeros of univariate complex polynomials. We prove some novel upper bounds fo...
متن کامل