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.

In this paper we propose a refinement of some successive overrelaxation methods based on the reverse Gauss–Seidel method for solving a system of linear equations Ax = b by the decomposition A = Tm − Em − Fm, where Tm is a banded matrix of bandwidth 2m + 1. We study the convergence of the methods and give software implementation of algorithms in Mathematica package with numerical examples.
ACM Computing Classification System (1998): G.1.3.
This paper is partly supported by project NI13...

This paper is partially supported by project ISM-4 of Department for Scientific Research,
“Paisii Hilendarski” University of Plovdiv.
In this paper we give methodological survey of “contemporary methods” for solving the nonlinear equation f(x) = 0. The reason for
this review is that many authors in present days rediscovered such classical methods. Here we develop one methodological schema for constructing nonstationary methods with a preliminary chosen speed of convergence.

2000 Mathematics Subject Classification: 65H10.
Here we give methodological survey of contemporary methods
for solving nonlinear systems of equations in Rn. The reason of this review
is that many authors in present days rediscovered such classical methods.
In particular, we consider Newton’s-type algorithms with sparse Jacobian.
Method for which the inverse matrix of the Jacobian is replaced by the
inverse matrix of the Vandermondian is proposed. A number of illustrative
numerical examples...

A modification of the Nekrassov method for finding a solution
of a linear system of algebraic equations is given and a numerical example
is shown.
* This paper is partly supported by project IS–M–4 of Department for Scientific Research,
Paisii Hilendarski University of Plovdiv.

This paper is dedicated to Prof. Nikolay Kyurkchiev
on the occasion of his 70th anniversary
This paper gives sufficient conditions for kth approximations of
the zeros of polynomial f (x) under which Kyurkchiev’s method fails on the
next step. The research is linked with an attack on the global convergence
hypothesis of this commonly used in practice method (as correlate hypothesis
for Weierstrass–Dochev’s method). Graphical examples are presented.

Никола Вълчанов, Тодорка Терзиева, Владимир Шкуртов, Антон Илиев -
Една от основните области на приложения на компютърната информатика е
автоматизирането на математическите изчисления. Информационните системи
покриват различни области като счетоводство, електронно обучение/тестване,
симулационни среди и т. н. Те работят с изчислителни библиотеки, които са специфични за обхвата на системата. Въпреки, че такива системи са перфектни и
работят безпогрешно, ако не се поддържат остаряват. В тази работа...

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