O polynomech, které mají jen reálné kořeny
O reálných polynomech 4. stupně
On a class of higher order methods for simultaneous rootfinding of generalized polynomials.
On a converse of Laguerre's theorem.
On A Fourth Order Wronskian Associated With Classical Orthogonal Polynomials
On a fourth order Wronskian associated with classical orthogonal polynomials.
On Condition Numbers and the Distance to the Nearest Ill-posed Problem.
On convergence of Börsch-Supan's method with Weierstrass' corrections.
On equations and properties concerning some classes of chordal polygons.
On H. Weyl and H. Minkowski polynomials.
On polynomials of Sheffer type arising from a Cauchy problem.
On realizability of sign patterns by real polynomials
The classical Descartes’ rule of signs limits the number of positive roots of a real polynomial in one variable by the number of sign changes in the sequence of its coefficients. One can ask the question which pairs of nonnegative integers , chosen in accordance with this rule and with some other natural conditions, can be the pairs of numbers of positive and negative roots of a real polynomial with prescribed signs of the coefficients. The paper solves this problem for degree polynomials.
On some properties of Hamel bases connected with the continuity of polynomial functions.
On stability and the Łojasiewicz exponent at infinity of coercive polynomials
In this article we analyze the relationship between the growth and stability properties of coercive polynomials. For coercive polynomials we introduce the degree of stable coercivity which measures how stable the coercivity is with respect to small perturbations by other polynomials. We link the degree of stable coercivity to the Łojasiewicz exponent at infinity and we show an explicit relation between them.
On stability of Alexander polynomials of knots and links (survey)
We study distribution of the zeros of the Alexander polynomials of knots and links in S³. After a brief introduction of various stabilities of multivariate polynomials, we present recent results on stable Alexander polynomials.
On stable polynomials
The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.
On the convergence of Halley-like method.
On the derivative and maximum modulus of a polynomial.
On the distribution of the number of real zeros of a random polynomial.
On the distribution on the roots of polynomials
Using classical results on conjugate functions, we give very short proofs of theorems of Erdös–Turán and Blatt concerning the angular distribution of the roots of polynomials. Then we study some examples.