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.

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

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.

Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].

About New Pattern Recognition Method for the Universal Program System “Recognition”

In this work the new pattern recognition method based on the unification of algebraic and statistical approaches is described. The main point of the method is the voting procedure upon the statistically weighted regularities, which are linear separators in two-dimensional projections of feature space. The report contains brief description of the theoretical foundations of the method, description of its software realization and the results of series of experiments proving its usefulness in practical tasks.

On The Critical Points of some Iteration Methods for Solving Algebraic Equations. Global Convergence Properties

In this work we give su±cient conditions for k-th approximations of the polynomial roots of f(x) when the Maehly{Aberth{Ehrlich, Werner-Borsch-Supan, Tanabe, Improved Borsch-Supan iteration methods fail on the next step. For these methods all non-attractive sets are found. This is a subsequent improvement of previously developed techniques and known facts. The users of these methods can use the results presented here for software implementation in Distributed Applications and Simulation Environ- ments. Numerical examples with graphics are shown.

On some Modifications of the Nekrassov Method for Numerical Solution of Linear Systems of Equations

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.