Superexponentially Convergent Algorithm for an Abstract Eigenvalue Problem with Applications to Ordinary Differential Equations.
In: Journal of Mathematical Sciences, Jg. 220 (2017-01-15), Heft 3, S. 273-300
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Zugriff:
A new algorithm for the solution of eigenvalue problems for linear operators of the form 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 $$ \overline{A}=A+\overline{B} $$ such that the eigenvalue problem for Ā is supposed to be simpler than for A: The algorithm for this eigenvalue problem is based on the homotopy idea and, for a given eigenpair number, recursively computes a sequence of approximate eigenpairs that converges to the exact eigenpair with a superexponential convergence rate. The eigenpairs can be computed in parallel for all prescribed indexes. The case of multiple eigenvalues of the operator Ā is emphasized. Examples of eigenvalue problems for the high-order ordinary differential operators are presented to support the theory. [ABSTRACT FROM AUTHOR]
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Titel: |
Superexponentially Convergent Algorithm for an Abstract Eigenvalue Problem with Applications to Ordinary Differential Equations.
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Autor/in / Beteiligte Person: | Gavrilyuk, I. ; Makarov, V. ; Romanyuk, N. |
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Zeitschrift: | Journal of Mathematical Sciences, Jg. 220 (2017-01-15), Heft 3, S. 273-300 |
Veröffentlichung: | 2017 |
Medientyp: | academicJournal |
ISSN: | 1072-3374 (print) |
DOI: | 10.1007/s10958-016-3184-4 |
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