Информационный анализ несовместных систем линейных алгебраических уравнений. Минимаксное решение
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Дата
2012
ORCID
DOI
Науковий ступінь
Рівень дисертації
Шифр та назва спеціальності
Рада захисту
Установа захисту
Науковий керівник
Члени комітету
Видавець
Технологический центр, Украинская государственная академия железнодорожного транспорта
Анотація
Предложен метод отыскания приближенного решения переопределенной несовместной системы линейных алгебраических уравнений (СЛАУ), для которого максимальная из невязок уравнений системы минимальна. Получены аналитические соотношения для расчета компонентов вектора. Приведены примеры.
The article concerns the acceptable solutions of incompatible systems of linear algebraic equations (SLAE), the necessity of which appears during the processing and information analysis of experimental data. There is an analysis of the efficiency of traditional approaches to the solution of similar problems, such as the least-squares method, which minimizes the norm of system residual, the method of input of correction vector of system second members. The alternative approach to the solution if incompatible SLAE was suggested. It consists in definition of regularizing algorithm for the given redefined SLAE, which makes it possible to get the approximate solution of the system, minimizing the norm of residual, for which the maximum of system equation residual is the minimum. The problem is reduced on each iteration to the finding of variables set, which provides modulo equality of all residuals for the system equations. The analytical ratios for direct calculation of components of desired set were obtained. The examples of calculations were given
The article concerns the acceptable solutions of incompatible systems of linear algebraic equations (SLAE), the necessity of which appears during the processing and information analysis of experimental data. There is an analysis of the efficiency of traditional approaches to the solution of similar problems, such as the least-squares method, which minimizes the norm of system residual, the method of input of correction vector of system second members. The alternative approach to the solution if incompatible SLAE was suggested. It consists in definition of regularizing algorithm for the given redefined SLAE, which makes it possible to get the approximate solution of the system, minimizing the norm of residual, for which the maximum of system equation residual is the minimum. The problem is reduced on each iteration to the finding of variables set, which provides modulo equality of all residuals for the system equations. The analytical ratios for direct calculation of components of desired set were obtained. The examples of calculations were given
Опис
Ключові слова
обработка данных, прикладные программы, численные методы решения, переопределенная несовместная система, минимаксный принцип, СЛАУ, system of linear algebraic equations, SLAE, vector of second member, least-squares method, correction vector, approximate solution, minimax principle, residual modulus, variables set, decision vector
Бібліографічний опис
Раскин Л. Г. Информационный анализ несовместных систем линейных алгебраических уравнений. Минимаксное решение / Л. Г. Раскин, О. В. Серая, Ю. В. Иванчихин // Восточно-европейский журнал передовых технологий. – 2012. – № 5/4. – С. 40-44.