A Note on the “Constructing” of Nonstationary Methods for Solving Nonlinear Equations with Raised Speed of Convergence

This paper is partially supported by project ISM-4 of Department for Scientific Research, “Paisii Hilendarski” University of Plovdiv.

Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions

2000 Mathematics Subject Classification: 47H04, 65K10.

Viability, Optimality and Stability of Dynamical Systems and Estimation of Convergence of Numerical Schemes

AMS subject classification: 49N35,49N55,65Lxx.

Algorithms for Finding Unitals and Maximal Arcs in Projective Planes of Order 16

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakalo ff , Sofia, July, 2006.

On Averaging Null Sequences of Real-Valued Functions

If ξ is a countable ordinal and (fk) a sequence of real-valued functions we define the repeated averages of order ξ of (fk). By using a partition theorem of Nash-Williams for families of finite subsets of positive integers it is proved that if ξ is a countable ordinal then every sequence (fk) of real-valued functions has a subsequence (f'k) such that either every sequence of repeated averages of order ξ of (f'k) converges uniformly to zero or no sequence of repeated averages of order ξ of (f'k) converges uniformly to zero. By the aid of this result we obtain some results stronger than Mazur’s theorem.

Generalization of Ehrlich-Kjurkchiev Method for Multiple Roots of Algebraic Equations

In this paper a new method which is a generalization of the Ehrlich-Kjurkchiev method is developed. The method allows to find simultaneously all roots of the algebraic equation in the case when the roots are supposed to be multiple with known multiplicities. The offered generalization does not demand calculation of derivatives of order higher than first simultaneously keeping quaternary rate of convergence which makes this method suitable for application from practical point of view.