Point estimation and the convergence of the Ehrlich-Aberth method.
Polynomial inequalities on general subsets of
Polynomial interpolation and asymptotic representations for zeta functions [Book]
Polynomials, sign patterns and Descartes' rule of signs
By Descartes’ rule of signs, a real degree polynomial with all nonvanishing coefficients with sign changes and sign preservations in the sequence of its coefficients () has positive and negative roots, where and . For , for every possible choice of the sequence of signs of coefficients of (called sign pattern) and for every pair satisfying these conditions there exists a polynomial with exactly positive and exactly negative roots (all of them simple). For this is not...
Prime rational functions
Let f(x) be a complex rational function. We study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we also derive some conditions for the case of complex polynomials.
Problems and Theorems in the Theory of Multiplier Sequences
The purpose of this paper is (1) to highlight some recent and heretofore unpublished results in the theory of multiplier sequences and (2) to survey some open problems in this area of research. For the sake of clarity of exposition, we have grouped the problems in three subsections, although several of the problems are interrelated. For the reader’s convenience, we have included the pertinent definitions, cited references and related results, and in several instances, elucidated the problems by...
Properties of functions in an auxiliary spline space.
-Eulerian polynomials and polynomials with only real zeros.
Quadratic Mean Radius of a Polynomial in C(Z)
* Dedicated to the memory of Prof. N. ObreshkoffA Schoenberg conjecture connecting quadratic mean radii of a polynomial and its derivative is verified for some kinds of polynomials, including fourth degree ones.
Ratio vectors of polynomial-like functions.
Reconnaître si un polynôme à plusieurs variables peut être décomposé en facteurs entiers
Reverse Markov inequality.
Root arrangements of hyperbolic polynomial-like functions.
A real polynomial P of degree n in one real variable is hyperbolic if its roots are all real. A real-valued function P is called a hyperbolic polynomial-like function (HPLF) of degree n if it has n real zeros and P(n) vanishes nowhere. Denote by xk(i) the roots of P(i), k = 1, ..., n-i, i = 0, ..., n-1. Then in the absence of any equality of the formxi(j) = xk(i) (1)one has∀i < j xk(i) < xk(j) < xk+j-i(i) (2)(the Rolle theorem). For n ≥ 4 (resp....
Safe convergence of Chebyshev-like method.
Safe convergence of Tanabe's method.
Some applications of Legendre numbers.
Some Coefficient Estimates for Polynomials on the Unit Interval
2000 Mathematics Subject Classification: 26C05, 26C10, 30A12, 30D15, 42A05, 42C05.In this paper we present some inequalities about the moduli of the coefficients of polynomials of the form f (x) : = еn = 0nan xn, where a0, ј, an О C. They can be seen as generalizations, refinements or analogues of the famous inequality of P. L. Chebyshev, according to which |an| Ј 2n-1 if | еn = 0n an xn | Ј 1 for -1 Ј x Ј 1.
Some integral properties of a general class of polynomials associated with Feynman integrals.
Some results concerning the zeros and coefficients of polynomials
Spectrum localization of regular matrix polynomials and functions.