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title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Newtonâs subdifferential method in Kaucher interval arithmetic - methodâs convergence research
Creators: name: Ð¢Ð¾Ð´Ð¾ÑÐ¾Ð²Ð°, ÐÐ½Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2021
Subjects: Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð°Ñ ÑÐ¸ÑÑÐµÐ¼Ð° Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÑ Ð°Ð»Ð³ÐµÐ±Â­ÑÐ°Ð¸ÑÐµÑÐºÐ¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹
ÑÑÐ±Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÐ¹ Ð¼ÐµÑÐ¾Ð´ ÐÑÑÑÐ¾Â­Ð½Ð°
Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð°Ñ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÐºÐ° ÐÐ°ÑÑ ÐµÑÐ°
ÑÐµÐ³ÑÐ»ÑÑÐ¸Ð·Ð°ÑÐ¸Ñ ÐÐ°Ð²ÑÐµÐ½Â­ÑÑÐµÐ²Ð°
Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð·
system of linear interval equations
Newtonâs subdifferential method
Kaucher interval arithmetic
Lavrentievâs regularization
interval analysis

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description: The given work is devoted to convergence researching of Newtonâs subdifferential method in Kaucher interval arithmetic. The research set the following goals: 1. Applying the theory of interval analysis, theoretically substantiate the usage of Newtonâs subdifferential method for problem solving of systems of linear interval equations. 2. Practically research subdifferential methodâs results of solving two systems of linear interval equations, that one of them is unsolvable. 3. Propose a reasonable method of systemâs correction in order to gain an optimal solution by subdifferential method for least changed data. Firstly, Newtonâs subdifferential method was applied for two systems of linear interval equations and returned two different results. Newtonâs subdifferential method excellently performed for one of them, while conducting an experiment by using of subdiff program, executed by Octave programming language. However, an experiment with a singular matrix in a given system did not perform well, demonstrating an oscillating sequence as a result. Secondly, Lavrentievâs regularization was failed at improving of the second system of linear interval equations. Consequently, another heuristic correction method was proposed and successfully applied.