Сибирский федеральный университет

Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций

Конференция: XIII International Scientific and Technical Conference "Applied Mechanics and Systems Dynamics"; Omsk; Omsk

Год издания: 2020

Аннотация: This article explores the accuracy of numerical solutions, and suggests methods foranalyzing accuracy depending on the properties of the problem. Numerical studies of complexexpensive objects of technology and physics require that the computational results be obtainedwith guaranteed accuracy. It also depends on the fact that in the work of technical objects thereare large intervals of operation time not observed experimentally. Therefore, there is a need todescribe the location of the observed and calculated values, as well as the accuracy with whichthey are calculated. The effect of strong growth in estimates of error bounds is manifested fora large number of methods used to estimate the error of a numerical solution. This means thelack of correctness of algorithms for evaluating the accuracy of numerical solutions due to thefailure of the stability conditions with respect to perturbations of the right-hand side. For manyproblems, among all the algorithms, the backward analysis of errors turned out to be the mosteffective method for assessing the accuracy of numerical solutions. The backward analysis oferrors consists in the fact that when assessing the accuracy (error) of a numerical solution, thenumerical solution is considered as an exact solution to a problem close to the original problem.A backward error analysis was proposed and developed in the algorithms of J Wilkinson in thecontext of the numerical solution of problems of linear algebra, and in the algorithms of V VVoevodin, who widely distributed it to many areas of numerical analysis. In the frameworkof the backward error analysis, the regularization of the algorithm for estimating the error ofa numerical solution is reasonably applied. This article explores methods for the backwardanalysis of errors of numerical solutions.

Журнал: Journal of Physics: Conference Series

Выпуск журнала: 1441

Номера страниц: 012165-012165

Издатель: IOP Publishing

• Rogalev A.N.
• Rogalev A.A. (Siberian Federal University)

• Ядро РИНЦ (eLIBRARY.RU)