title: Ð ÐµÑÐµÐ½Ð¸Ðµ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾ Ð´Ð¾Ð¿ÑÑÐºÐ°Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ ÑÐ°ÑÐ¿Ð¾Ð·Ð½Ð°ÑÑÐµÐ³Ð¾ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»Ð°
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: Solving the interval linear tolerance problem by the recognizing functional method
Creators: name: Ð¡Ð¼Ð¾Ð»ÑÑÐºÐ¸Ð¹, ÐÐ°ÐºÑÐ¸Ð¼
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: 2020
Subjects: Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð°Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ Ð·Ð°Ð´Ð°ÑÐ° Ð¾ Ð´Ð¾Ð¿ÑÑÐºÐ°Ñ
Ð¼ÐµÑÐ¾Ð´ ÑÐ°ÑÐ¿Ð¾Ð·Ð½Ð°ÑÑÐµÐ³Ð¾ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»Ð°
Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð° tolsolvty
interval linear tolerance problem
recognizing functional method
program tolsolvty

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ, Ð¿Ð¾ÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¸ ÑÑÐºÐ¾ÑÐµÐ½Ð¸Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ tolsolvty, ÐºÐ¾ÑÐ¾ÑÐ°Ñ Ð¿Ð¾Ð»Ð½Ð¾ÑÑÑÑ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐµÑ ÑÐ°Ð·ÑÐµÑÐ¸Ð¼Ð¾ÑÑÑ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾ Ð´Ð¾Ð¿ÑÑÐºÐ°Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ ÑÐ°ÑÐ¿Ð¾Ð·Ð½Ð°ÑÑÐµÐ³Ð¾ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»Ð°. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ð¾ÑÑÐ¸ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ tolsolvty. 2. ÐÐ°ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ðµ ÑÑÐ¿ÐµÑÐ´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»Ð° ÑÐ°ÑÐ¿Ð¾Ð·Ð½Ð°ÑÑÐµÐ³Ð¾ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»Ð° Ð´Ð»Ñ Ð¾Ð±Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð¸Ñ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ ÐµÐ³Ð¾ ÑÑÐ¿ÐµÑÐ³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ° Ð² Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ðµ tolsolvty. 3. ÐÐ¾ÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ tolsolvty Ð½Ð° ÑÐ·ÑÐº Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Python. 4. Ð£ÑÐºÐ¾ÑÐµÐ½Ð¸Ðµ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¹ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ tolsolvty. ÐÑÐ»Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¸ Ð²ÑÑÐ¸ÑÐ»Ð¸ÑÐµÐ»ÑÐ½ÑÐµ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÑ Ð¿Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ ÑÐ¸Ð¿Ð¾Ð²ÑÑ Ð·Ð°Ð´Ð°Ñ Ð¼Ð°Ð»Ð¾Ð¹, ÑÑÐµÐ´Ð½ÐµÐ¹ Ð¸ Ð±Ð¾Ð»ÑÑÐ¾Ð¹ ÑÐ°Ð·Ð¼ÐµÑÐ½Ð¾ÑÑÐµÐ¹, ÑÐ³ÐµÐ½ÐµÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ ÑÐ»ÑÑÐ°Ð¹Ð½ÑÐ¼ Ð¾Ð±ÑÐ°Ð·Ð¾Ð¼, Ð´Ð»Ñ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¼ÐµÐ¶Ð¾ÑÑÐ°ÑÐ»ÐµÐ²Ð¾Ð³Ð¾ ÑÐºÐ¾Ð½Ð¾Ð¼Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð±Ð°Ð»Ð°Ð½ÑÐ° Ð½Ð° ÑÐ·ÑÐºÐ°Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ MATLAB, GNU Octave, Scilab Ð¸ Python. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð±ÑÐ»Ð¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ Ð»ÐµÐ³ÐºÐ¾ Ð¿ÑÐ¾Ð²ÐµÑÑÐµÐ¼Ð¾Ðµ ÑÑÐ»Ð¾Ð²Ð¸Ðµ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ð¾ÑÑÐ¸ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ tolsolvty Ð¸ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð´Ð»Ñ Ð½Ð°ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ñ ÑÑÐ¿ÐµÑÐ´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»Ð° ÑÐ°ÑÐ¿Ð¾Ð·Ð½Ð°ÑÑÐµÐ³Ð¾ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»Ð° â Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð° tolsolvty ÐºÐ¾ÑÑÐµÐºÑÐ½Ð¾ Ð²ÑÑÐ¸ÑÐ»ÑÐµÑ ÐµÐ³Ð¾ ÑÑÐ¿ÐµÑÐ³ÑÐ°Ð´Ð¸ÐµÐ½Ñ. ÐÐ°Ð¿Ð¸ÑÐ°Ð½Ð° ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ tolsolvty Ð½Ð° ÑÐ·ÑÐºÐµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Python. ÐÐ¾ Ð¼Ð½Ð¾Ð³Ð¾ ÑÐ°Ð· ÑÑÐºÐ¾ÑÐµÐ½Ñ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ tolsolvty Ð½Ð° ÑÐ·ÑÐºÐ°Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ MATLAB, GNU Octave, Scilab Ð¸ Python.
description: The given work is devoted to studying, porting and speeding up the program tolsolvty, which completely determines the solvability of the interval linear tolerance problem by the recognizing functional method. The research set the following goals: 1. Studying the applicability of the program tolsolvty. 2. Finding the superdifferential of the recognizing functional to justify the calculation of its supergradient in the program tolsolvty. 3. Porting the program tolsolvty to the programming language Python. 4. Speeding up the program tolsolvty implementations. Mathematical researches and computational experiments to solve typical problems of small, medium and large dimensions, randomly generated, for an interval input-output model in the programming languages MATLAB, GNU Octave, Scilab and Python were made. The study resulted into getting an easily verifiable condition for the applicablity of the program tolsolvty and an algorithm for finding the superdifferential of the recognizing functional â it was shown, that the program tolsolvty correctly calculates its supergradient. The implementation of the program tolsolvty was written in the programming language Python. The implementations of the program tolsolvty in the programming languages MATLAB, GNU Octave, Scilab and Python were sped up many times.