A conjecture of Schoenberg.
A criterion for unimodality.
A factorisation of the Askey’s characteristic function
A new look at Newton's inequalities.
A new proof of a theorem about generalized orthogonal polynomials.
A note on Babylonian square-root algorithm and related variants.
A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix
It is shown that if A is a bounded linear operator on a complex Hilbert space, then , where w(A) and ||A|| are the numerical radius and the usual operator norm of A, respectively. An application of this inequality is given to obtain a new estimate for the numerical radius of the Frobenius companion matrix. Bounds for the zeros of polynomials are also given.
A pseudo Laguerre method
A simple proof of the Fundamental Theorem of Algebra
In the paper an elementary and simple proof of the Fundamental Theorem of Algebra is given.
A Unified Approach to Methods for the Simultaneous Computation of All Zeros of Generalized Polynomials.
Algoritmy na výpočet kořenů polynomu
An extension of the root perturbation -dimensional polynomial factorization method
An Implementation of Vincent's Theorem.
Are the coefficients of a polynomial well-conditioned functions of its roots?
Behavior of the trinomial arcs when .
Bounds of the roots of the real polynomial
An algorithm for the calculation of a lower bound of the absolute values of the roots of a real algebraic polynomial, of an arbitrary degree, is derived. An example is given to compare the bounds calculated by the method proposed and by other methods.
Braiding of the attractor and the failure of iterative algorithms.
Complex Analogues of the Rolle's Theorem
2000 Mathematics Subject Classification: 30C10.Classical Rolle’s theorem and its analogues for complex algebraic polynomials are discussed. A complex Rolle’s theorem is conjectured.
Complexité et géométrie réelle
Computing amoebas.