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Well-rounded lattices via polynomials with real roots
(2020-01-01)
Well-rounded lattices have been a topic of recent studies with applications in wiretap channels and in cryptography. A lattice of full rank in Euclidean space is called well-rounded if its set of minimal vectors spans the ...
On the minimum of a positive polynomial over the standard simplex
(Academic Press Ltd - Elsevier Science Ltd, 2010-04)
We present a new positive lower bound for the minimum value taken by a polynomial P with integer coefficients in k variables over the standard simplex of Rk, assuming that P is positive on the simplex. This bound depends ...
Inequalities for the Extended Best Polynomial Approximation Operator in Orlicz Spaces
(Springer Heidelberg, 2019-02)
In this paper we pursue the study of the best approximation operator extended from L^Φ to L^φ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best ...
The roots of a polynomial depend continuously on its coefficients
(Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas, 1994)
An elementary proof is given of the continuous dependence of the roots of a polynomial on its coefficients.
On computational aspects of discrete Sobolev inner products on the unit circle
(2013-09-17)
In this paper, we show how to compute in O(n2) steps the Fourier coefficients associated with the Gelfand-Levitan approach for discrete Sobolev orthogonal polynomials on the unit circle when the support of the discrete ...
On computational aspects of discrete Sobolev inner products on the unit circle
(2013-09-17)
In this paper, we show how to compute in O(n2) steps the Fourier coefficients associated with the Gelfand-Levitan approach for discrete Sobolev orthogonal polynomials on the unit circle when the support of the discrete ...