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

Iliev, Anton — 1998

Serdica Mathematical Journal

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.

A Refinement of some Overrelaxation Algorithms for Solving a System of Linear Equations

Kyurkchiev, NikolayIliev, Anton — 2013

Serdica Journal of Computing

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...

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

Kyurkchiev, NikolayIliev, Anton — 2009

Serdica Journal of Computing

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.

A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations

Kyurkchiev, NikolayIliev, Anton — 2007

Serdica Mathematical Journal

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...

On the Critical Points of Kyurkchiev’s Method for Solving Algebraic Equations

Valchanov, NikolaGolev, AngelIliev, Anton — 2015

Serdica Journal of Computing

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.

Architecture of Extensible Computations Driven Systems Архитектура на разширяеми, управлявани от изчисления системи

Valchanov, NikolaTerzieva, TodorkaShkurtov, VladimirIliev, Anton — 2010

Union of Bulgarian Mathematicians

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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