Ein numerisches Verfahren zur simultanen Ermittlung aller Nullstellen eines Polynoms.
Enclosing roots of polynomial equations and their applications to iterative processes.
Error Analysis of Splitting Algorithms for Polynomials.
Estimation of polynomial roots by continued fractions
Even and Old Overdetermined Strata for Degree 6 Hyperbolic Polynomials
2000 Mathematics Subject Classification: 12D10.In the present paper we consider degree 6 hyperbolic polynomials (HPs) in one variable (i.e. real and with all roots real). We are interested in such HPs whose number of equalities between roots of the polynomial and/or its derivatives is higher than expected. We give the complete study of the four families of such degree 6 even HPs and also of HPs which are primitives of degree 5 HPs.Research partially supported by research project 20682 for cooperation...
Explicit polar decomposition of companion matrices.
Extention of Apolarity and Grace Theorem
MSC 2010: 30C10The classical notion of apolarity is defined for two algebraic polynomials of equal degree. The main property of two apolar polynomials p and q is the classical Grace theorem: Every circular domain containing all zeros of p contains at least one zero of q and vice versa. In this paper, the definition of apolarity is extended to polynomials of different degree and an extension of the Grace theorem is proved. This leads to simplification of the conditions of several well-known results...