On Differential Inclusions with Unbounded Right-Hand Side

2000 Mathematics Subject Classification: 58C06, 47H10, 34A60.

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.

Uniform Convergence of the Newton Method for Aubin Continuous Maps

* This work was supported by National Science Foundation grant DMS 9404431.

Application of the Heterogeneous System Prediction Method to Pattern Recognition Problem

* This work was financially supported by RFBR-04-01-00858.

Application of the Multivariate Prediction Method to Time Series

* This work was financially supported by RFBR-04-01-00858.

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.

Method for Analytical Representation of the Maximum Inaccuracies of Indirectly Measurable Variable

Let us have an indirectly measurable variable which is a function of directly measurable variables. In this survey we present the introduced by us method for analytical representation of its maximum absolute and relative inaccuracy as functions, respectively, of the maximum absolute and of the relative inaccuracies of the directly measurable variables. Our new approach consists of assuming for fixed variables the statistical mean values of the absolute values of the coefficients of influence, respectively, of the absolute and relative inaccuracies of the directly measurable variables in order to determine the analytical form of the maximum absolute and relative inaccuracies of an indirectly measurable variable. Moreover, we give a method for determining the numerical values of the maximum absolute and relative inaccuracies. We define a sample plane of the ideal perfectly accurate experiment and using it we give a universal numerical characteristic – a dimensionless scale for determining the quality (accuracy) of the experiment.

The Graves Theorem Revisited II: Robust Convergence of the Newton Method

AMS subject classification: 65J15, 47H04, 90C30.

A Fast Algorithm for Weber Problem on a Grid

AMS subject classification: 90B80.

Local-Median Method of Forecasting for Regression Time Series under Outliers

2002 Mathematics Subject Classification: 62M20, 62-07, 62J05, 62P20.

Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast

2000 Mathematics Subject Classification: Primary 60G55; secondary 60G25.