Nikolay Kyurkchiev

On the Hausdorff distance between the Heaviside step function and Verhulst logistic function

In this note we prove more precise estimates for the approximation of the step function by sigmoidal logistic functions. Numerical examples, illustrating our results are given, too.

On the approximation of the step function by some sigmoid functions

In this note the Hausdorff approximation of the Heaviside step function by several sigmoid functions (log–logistic, transmuted log–logistic and generalized logistic functions) is considered and precise upper and lower bounds for the Hausdorff distance are obtained. Numerical examples, that illustrate our results are given, too.

On Some Multipoint Methods Arising from Optimal in the Sense of Kung–Traub Algorithms

In this paper we will examine self-accelerating in terms of convergence speed and the corresponding index of efficiency in the sense of Ostrowski–Traub of certain standard and most commonly used in practice multipoint iterative methods using several initial approximations for numerical solution of nonlinear equations due to optimal in the sense of the Kung–Traub algorithm of order 4, 8 and 16. Some hypothetical iterative procedures generated by algorithms from order of convergence 32 and 64 are also studied (the receipt and publication of which is a matter of time, having in mind the increased interest in such optimal algorithms). The corresponding model theorems for their convergence speed and efficiency index have been formulated and proved.

On a Generalization of the Euler-Chebyshev Method for Simultaneous Extraction of Only a Part of All Roots of Polynomials

We propose a method with raised speed of convergence for simultaneous extraction of a part of all roots of polynomials. The method is efficient for the polynomials which have well separated real roots. The proof of local convergence is shown and numerical results are given.

On the numerical solution of the general kinetic “K-angle” reaction system

In a recent paper by Tobias and Tasi in this journal the authors discuss the “K-angle” kinetic problem and focus on its analytic solution for

80th Anniversary of the birth of Prof. Donald Knuth (1938)

K\le 5

The dynamics and control of a singular biological economic model with stage structure. Some moduli in programming environment Mathematica

K≤5. The authors correctly mention that the case