title: ÐÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð°Ñ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ° Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð°ÑÑÐ¸Ð½Ð½Ð¾Ð¹ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÐºÐ¸ Ð´Ð»Ñ Ð²ÐµÐ´ÐµÐ½Ð¸Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐ¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹
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: A software library based on affine arithmetic for mathematical processing of measurement results
Creators: name: ÐÐµÐ¼ÑÐµÐ½ÐºÐ¾, ÐÐ¼Ð¸ÑÑÐ¸Ð¹
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°ÑÑÐ¸Ð½Ð½Ð°Ñ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÐºÐ°
MATLAB
Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐ° Ð½ÐµÑÐ¾ÑÐ½ÑÑ Ð´Ð°Ð½Ð½ÑÑ
Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ°Ð¼Ð¸ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹
affine arithmetics
processing of inaccurate data
calculations with measurement results

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«ÐÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð°Ñ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ° Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð°ÑÑÐ¸Ð½Ð½Ð¾Ð¹ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÐºÐ¸ Ð´Ð»Ñ Ð²ÐµÐ´ÐµÐ½Ð¸Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐ¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹Â». ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð¹ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸, ÑÐµÐ°Ð»Ð¸Ð·ÑÑÑÐµÐ¹ Ð°ÑÑÐ¸Ð½Ð½ÑÑ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÐºÑ, Ð´Ð»Ñ Ð½ÑÐ¶Ð´ ÑÐ¾Ð¿ÑÐ¾Ð²Ð¾Ð¶Ð´ÐµÐ½Ð¸Ñ ÑÐ°ÑÑÐµÑÐ¾Ð² Ñ Ð½ÐµÑÐ¾ÑÐ½ÑÐ¼Ð¸ Ð´Ð°Ð½Ð½ÑÐ¼Ð¸ Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¾ÑÐµÐ½ÐºÐ¾Ð¹ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸Ðº Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÐ¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ð¹ Ð´Ð»Ñ ÑÑÐµÐ´Ñ ÑÐ°Ð·ÑÐ°Ð±ÑÐºÐ¸ MATLAB. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ. 1) ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ñ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¹ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÐºÐ¸. 2) ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ñ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¹ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐº Ð´Ð»Ñ ÑÐ°Ð±Ð¾ÑÑ Ñ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»Ð°Ð¼Ð¸. 3) Ð¤Ð¾ÑÐ¼ÑÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÑ ÑÑÐµÐ±Ð¾Ð²Ð°Ð½Ð¸Ð¹, ÑÑÐ¸ÑÑÐ²Ð°ÐµÐ¼ÑÑ Ð¿ÑÐ¸ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸ Ð´Ð»Ñ Ð½ÑÐ¶Ð´ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐ¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹. 4) ÐÐ¾Ð»ÑÑÐµÐ½Ð¸Ðµ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¸ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² ÑÐ°Ð±Ð¾ÑÑ Ñ Ð°ÑÑÐ¸Ð½Ð½ÑÐ¼Ð¸ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»Ð°Ð¼Ð¸. 5) Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸, ÑÐµÐ°Ð»Ð¸Ð·ÑÑÑÐµÐ¹ Ð²ÑÐµ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÐµ Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼ÑÐµ ÑÑÐ½ÐºÑÐ¸Ð¸ Ð¸ Ð¾Ð¿ÐµÑÐ°ÑÐ¸Ð¸ Ð¿ÑÐ¸ ÑÐ°Ð±Ð¾ÑÐµ Ñ Ð°ÑÑÐ¸Ð½Ð½ÑÐ¼Ð¸ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»Ð°Ð¼Ð¸. 6) Ð­ÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½Ð¾Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½Ð¾Ð¹ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½ÑÑ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¹ Ð°ÑÑÐ¸Ð½Ð½Ð¾Ð¹ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÐºÐ¸. ÐÐ·ÑÑÐµÐ½Ð° ÑÐµÑÐ½Ð¾Ð»Ð¾Ð³Ð¸Ñ ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½ÑÑ Ð¿Ð°ÐºÐµÑÐ¾Ð² Ð² ÑÑÐµÐ´Ðµ MATLAB. ÐÑÐ» ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½ÑÐ¹ Ð¿Ð°ÐºÐµÑ, Ð¿ÑÐµÐ´Ð¾ÑÑÐ°Ð²Ð»ÑÑÑÐ¸Ð¹ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÑ Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸Ð·Ð°ÑÐ¸Ð¸ ÑÐ°Ð±Ð¾ÑÑ Ñ Ð½ÐµÑÐ¾ÑÐ½ÑÐ¼Ð¸ Ð´Ð°Ð½Ð½ÑÐ¼Ð¸, Ð²ÐºÐ»ÑÑÐ°Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹, ÑÑÐµÐ´ÑÑÐ²Ð°Ð¼Ð¸ Ð°ÑÑÐ¸Ð½Ð½Ð¾Ð¹ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÐºÐ¸. Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð°Ñ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ° Ð¿Ð¾Ð´ Ð½Ð°Ð·Ð²Ð°Ð½Ð¸ÐµÐ¼ Â«affintÂ». ÐÑÐ»Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½ÑÑ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½ÑÑ ÑÑÐµÐ´ÑÑÐ². ÐÑÐ»Ð¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐµ Ð¿Ð¾Ð´ÑÐ²ÐµÑÐ¶Ð´ÐµÐ½Ð¸Ñ ÐºÐ¾ÑÑÐµÐºÑÐ½Ð¾ÑÑÐ¸ ÑÐ°Ð±Ð¾ÑÑ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½Ð¾Ð¹ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸, Ð° ÑÐ°ÐºÐ¶Ðµ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÐµ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ¸ Ð±ÑÑÑÑÐ¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ ÑÐ°ÑÑÐµÑÐ¾Ð², Ð²ÑÐ¿Ð¾Ð»Ð½ÑÐµÐ¼ÑÑ Ñ ÐµÐµ Ð¿Ð¾Ð¼Ð¾ÑÑÑ.
description: Theme of the final qualification work: âA software library based on affine arithmetic for mathematical processing of measurement resultsâ. This work is devoted to the development of a software library that implements affine arithmetic for the needs of supporting calculations with inaccurate data by automatically estimating the error characteristics of calculation results for the MATLAB development environment. Tasks that were solved in the course of work. 1) Analysis of existing modifications of interval arithmetic. 2) Study of existing library implementations for working with intervals. 3) Formulation of the basic requirements taken into account when developing the library for the needs of mathematical processing of measurement results. 4) Obtaining methods and algorithms for working with affine intervals. 5) Development of a library that implements all the basic necessary functions and operations when working with affine intervals. 6) An experimental study of the developed library. The analysis of existing software implementations of affine arithmetic is carried out. The technology of creating software packages in the MATLAB environment is studied. A software package was developed that provides the ability to automate work with inaccurate data, including measurement results, using affine arithmetic. A software library called âaffintâ has been developed. Experimental studies of the developed software were conducted. Experimental confirmations of the correctness of the developed library were obtained, as well as temporal characteristics of the speed of calculations performed with its help.