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The numerical stability of two-level and three-level iterative methodsстатья
Информация о цитировании статьи получена из
Scopus
Дата последнего поиска статьи во внешних источниках: 28 мая 2015 г.
- Авторы: Nikolaev E.S., Samarskii A.A.
- Журнал: USSR Computational Mathematics and Mathematical Physics
- Том: 12
- Номер: 5
- Год издания: 1972
- Первая страница: 140
- Последняя страница: 154
- DOI: 10.1016/0041-5553(72)90008-0
- Аннотация: The problem of the numerical stability of two-level and three-level iterative processes in solving the linear operator equation of the first kind Au = f in Hilbert space is considered. One of the problems of the theory of iterative processes is that of obtaining quantitative characteristics enabling methods of different structure to be compared. In theoretical investigations the criterion of comparison of methods by the number of iterations, on the assumption that all the iterations are carried out exactly, is most often used. However, in a practical computational method the process of rounding the results of arithmetical operations introduces some errors into the solution at each stage. This fact leads to the necessity to compare iterative methods by their numerical accuracy. In the present paper this characteristic is considered for two-level (simple iteration) and three-level (semi-iterative Chebyshev and stationary) iterative processes. In the investigation it is assumed that the introduction of a rounding error is equivalent to a perturbation of the input data of the iterative scheme. This approach, which enables the problem of the numerical accuracy of the method to be reduced to a study of the stability with respect to the input data of some perturbed problem, was used in [4] when considering an abstract scheme of a two-level iterative process. The estimates obtained prove the numerical stability of the iterative schemes considered. It is shown that the coefficients in the estimates depend only on the dimensionless parameter ξ = γ1/γ2, where γ1 and γ2 are the limits of the spectrum of the operator A or constants of equivalence of the operator A and a second operator B of the iterative scheme.
- Добавил в систему: Николаев Евгений Сергеевич