title: ÐÑÐµÑÐ°ÑÐ¸Ð¾Ð½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ ÑÐµÑÐµÐ½Ð¸Ñ ÑÐ¸ÑÑÐµÐ¼ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÑ Ð°Ð»Ð³ÐµÐ±ÑÐ°Ð¸ÑÐµÑÐºÐ¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹
title: ÑÑÐµÐ±Ð½Ð¾Ðµ Ð¿Ð¾ÑÐ¾Ð±Ð¸Ðµ
titleType: Subtitle
title: Iterative methods for solving linear systems
Creators: name: ÐÑÑÑ, ÐÐ°Ð»ÐµÐ½ÑÐ¸Ð½Ð°
name: ÐÐ¾Ð±ÑÐµÑÐ¾Ð²Ð°, Ð¡Ð²ÐµÑÐ»Ð°Ð½Ð°
name: ÐÐ½ÑÑÑÐ¸ÐµÐ², ÐÐ³Ð¾ÑÑ
Publisher: name: ÐÐÐÐÐ¢ÐÐ¥-ÐÐ ÐÐ¡Ð¡
Year: 2025
Subjects: ÐÐ»Ð³ÐµÐ±ÑÐ°Ð¸ÑÐµÑÐºÐ¸Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ
ÐÐ¸Ð½ÐµÐ¹Ð½ÑÐµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ
ÐÑÐµÑÐ°ÑÐ¸Ñ

description: Ð¡Ð¾Ð¾ÑÐ²ÐµÑÑÑÐ²ÑÐµÑ ÑÐ¾Ð´ÐµÑÐ¶Ð°Ð½Ð¸Ñ Ð½Ð°Ð¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ð¹ Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÑÐºÐ¾Ð¹ Ð¿Ð¾Ð´Ð³Ð¾ÑÐ¾Ð²ÐºÐ¸ 01.03.02 Â«ÐÑÐ¸ÐºÐ»Ð°Ð´Ð½Ð°Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÐºÐ° Ð¸ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸ÐºÐ°Â». Ð Ð°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÑÑÑ Ð·Ð°Ð´Ð°ÑÐ° ÑÐµÑÐµÐ½Ð¸Ñ ÑÐ¸ÑÑÐµÐ¼ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÑ Ð°Ð»Ð³ÐµÐ±ÑÐ°Ð¸ÑÐµÑÐºÐ¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹. Ð Ð°Ð·Ð±Ð¸ÑÐ°ÑÑÑÑ Ð¸ÑÐµÑÐ°ÑÐ¸Ð¾Ð½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð´Ð°Ð½Ð½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸: ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½ÑÐµ Ð¸ Ð½ÐµÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½ÑÐµ. ÐÐ¾Ð´ÑÐ¾Ð±Ð½Ð¾ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÑÑÑ Ð¼ÐµÑÐ¾Ð´ Ð¿ÑÐ¾ÑÑÑÑ Ð¸ÑÐµÑÐ°ÑÐ¸Ð¹: ÑÐ¾ÑÐ¼ÑÐ»Ð¸ÑÑÑÑÑÑ Ð¸ Ð´Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÑÑÑÑ ÑÐµÐ¾ÑÐµÐ¼Ñ Ð¾ ÐµÐ³Ð¾ ÑÑÐ¾Ð´Ð¸Ð¼Ð¾ÑÑÐ¸, Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑÑÑ ÑÐ¿Ð¾ÑÐ¾Ð±Ñ Ð¿ÑÐ¸Ð²ÐµÐ´ÐµÐ½Ð¸Ñ ÑÐ¸ÑÑÐµÐ¼Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ðº Ð²Ð¸Ð´Ñ, ÑÐ´Ð¾Ð±Ð½Ð¾Ð¼Ñ Ð´Ð»Ñ Ð¸ÑÐµÑÐ°ÑÐ¸Ð¹. Ð Ð°Ð·Ð±Ð¸ÑÐ°ÐµÑÑÑ Ð¼ÐµÑÐ¾Ð´ Ð¯ÐºÐ¾Ð±Ñ, Ð¼ÐµÑÐ¾Ð´ Ð¸ÑÐµÑÐ°ÑÐ¸Ð¹ ÐÐµÐ¹ Ð´ÐµÐ» Ñ Ð¸ Ð¼ÐµÑÐ¾Ð´ ÑÐµÐ»Ð°ÐºÑÐ°ÑÐ¸Ð¹, ÐºÐ°Ðº ÑÐ°ÑÑÐ½ÑÐµ ÑÐ»ÑÑÐ°Ð¸ Ð¼ÐµÑÐ¾Ð´Ð° Ð¿ÑÐ¾ÑÑÑÑ Ð¸ÑÐµÑÐ°ÑÐ¸Ð¹. ÐÐ¾ÐºÐ°Ð·ÑÐ²Ð°ÑÑÑÑ ÑÐµÐ¾ÑÐµÐ¼Ñ Ð¾ ÑÑÐ¾Ð´Ð¸Ð¼Ð¾ÑÑÐ¸ Ð´Ð°Ð½Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð². Ð ÐºÐ°ÑÐµÑÑÐ²Ðµ Ð½ÐµÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐµÑÐµÐ½Ð¸Ñ ÑÐ¸ÑÑÐµÐ¼ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÑ Ð°Ð»Ð³ÐµÐ±ÑÐ°Ð¸ÑÐµÑÐºÐ¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð¿ÑÐ¸Ð²Ð¾Ð´Ð¸ÑÑÑ Ð¼ÐµÑÐ¾Ð´ Ð Ð¸ÑÐ°ÑÐ´ÑÐ¾Ð½Ð°, Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ½ÑÐ¹ Ð¼ÐµÑÐ¾Ð´ Ð¸ Ð¼ÐµÑÐ¾Ð´ ÑÐ¾Ð¿ÑÑÐ¶ÐµÐ½Ð½ÑÑ Ð½Ð°Ð¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ð¹. Ð Ð°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÑÑÑÑ Ð±Ð°Ð·Ð¾Ð²ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ Ð¿ÑÐµÐ´Ð¾Ð±ÑÐ³Ð» Ð¾ Ð²Ð»Ð¸Ð²Ð°Ð½Ð¸Ñ Ð´Ð»Ñ ÑÑÐºÐ¾ÑÐµÐ½Ð¸Ñ Ð¸ÑÐµÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ Ð¿ÑÐ¾ÑÐµÑÑÐ°. Ð Ð¿Ð¾ÑÐ¾Ð±Ð¸Ð¸ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½ ÑÐ°Ð·Ð´ÐµÐ» Ðµ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸ÐµÐ¼ Ð»Ð°Ð±Ð¾ÑÐ°ÑÐ¾ÑÐ½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: ÑÐ¾ÑÐ¼ÑÐ»Ð¸ÑÑÐµÑÑÑ Ð·Ð°Ð´Ð°Ð½Ð¸Ðµ Ð¸ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½ÑÐµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ, Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ñ Ð²Ð°ÑÐ¸Ð°Ð½ÑÑ Ð¸ Ð¿ÑÐ¸Ð¼ÐµÑÑ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ. ÐÑÐµÐ´Ð½Ð°Ð·Ð½Ð°ÑÐµÐ½Ð¾ Ð´Ð»Ñ ÑÑÑÐ´ÐµÐ½ÑÐ¾Ð², Ð¸Ð·ÑÑÐ°ÑÑÐ¸Ñ Ð´Ð¸ÑÑÐ¸Ð¿Ð»Ð¸Ð½Ñ Â«Ð§Ð¸ÑÐ»ÐµÐ½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´ÑÂ», Ð° ÑÐ°ÐºÐ¶Ðµ Ð´Ð»Ñ Ð¿ÑÐµÐ¿Ð¾Ð´Ð°Ð²Ð°ÑÐµÐ»ÐµÐ¹ Ð¸ Ð¸Ð½Ð¶ÐµÐ½ÐµÑÐ¾Ð², Ð´ÐµÑÑÐµÐ»ÑÐ½Ð¾ÑÑÑ ÐºÐ¾ÑÐ¾ÑÑÑ ÑÐ²ÑÐ·Ð°Ð½Ð° Ðµ Ð²Ð¾Ð¿ÑÐ¾ÑÐ°Ð¼Ð¸ Ð²ÑÑÐ¸ÑÐ»Ð¸ÑÐµÐ»ÑÐ½Ð¾Ð¹ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÐºÐ¸.
description: The training manual corresponds to the content of the Bachelorâs degree majors 01.03.02 âApplied Mathematics and Informaticsâ. The authors consider the problem of solving linear systems. Iterative methods of solving this problem are analyzed: stationary and non-stationarv. The fixed point iteration method is deesribed in detail. Theorems on its convergence are formulated and proved. Methods for bringing a linear system to a form convenient for iterations are described. The Jacobi, the Gauss-Seidel and the relaxation methods are analyzed as special eases of the fixed point iteration method. Convergence theorems are formulated and proved. As non-stationarv methods the Richardson method, the gradient method, and the conjugate gradient method are described. Basie preconditioning methods for speeding up the iterative process are presented. In addition, the manual includes a section describing laboratory work. It contains the problem statement and possible investigations, variants and examples. It is intended for students studying the discipline âNumerical methodsâ as well as for teachers and engineers whose area of interest is related to computational mathematics and numerical methods.