Superexponentially convergent algorithm for an abstract eigenvalue problem with applications to ODEs
A new algorithm for eigenvalue problems for the linear operators of the type A = A + B with a special application to high order ordinary differential equations is proposed and justified. The algorithm is based on the approximation of A by an operator A¯ = A + B¯ where the eigenvalue problem for A¯ i...
Збережено в:
| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2015 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2015
|
| Назва видання: | Нелінійні коливання |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/177219 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Цитувати: | Superexponentially convergent algorithm for an abstract eigenvalue problem with applications to ODEs / I.P. Gavrilyuk, V.L. Makarov, N.M. Romanyuk // Нелінійні коливання. — 2015. — Т. 18, № 3. — С. 332-356 — Бібліогр.: 23 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | A new algorithm for eigenvalue problems for the linear operators of the type A = A + B with a special application to high order ordinary differential equations is proposed and justified. The algorithm is based on the approximation of A by an operator A¯ = A + B¯ where the eigenvalue problem for A¯ is supposed to be simpler then that for A. The algorithm for this eigenvalue problem is based on the homotopy idea and for a given eigenpair number computes recursively a sequence of the approximate eigenpairs which converges to the exact eigenpair with an superexponential convergence rate. The eigenpairs can be computed in parallel for all prescribed indexes. The case of multiple eigenvalues of the operator A¯ is emphasized. Examples of the eigenvalue problems for the high order ordinary differential operators are presented to support the theory. |
|---|