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 The Impact of Multiplication Operators on the Ill-Posedness of Inverse Problems
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The Impact of Multiplication Operators on the Ill-Posedness of Inverse Problems

автор Melina F. издательство Книга по Требованию Математический анализ. Кратные и криволинейные интегралы. Задачи, решения
Cтраниц 168        мягкая обложка       
Аннотация:We provide a conjecture, verified by several numerical studies, how those operators influence the singular values. Then the local degree of ill-posedness is investigated via the Frechet derivative, providing the situation described above. This case occurs, for example, for nonlinear operator equations. In this context we also provide a short summary on the relationship between nonlinear problems and their linearizations. If the multiplier function has got zeroes, the determination of the local degree of ill-posedness is not trivial. Finally, we analyze the influence of these multiplication operators on Tikhonov regularization and corresponding convergence rates. We are going to investigate this situation, provide analytical tools as well as their limitations. In this work we deal with the degree of ill-posedness of linear operators in Hilbert spaces, where the operator may be decomposed into a compact linear integral operator with a well-known decay rate of singular values and a multiplication operator. By using several numerical approaches for computing the singular values we find that the degree of ill-posedness does not change through those multiplication operators.
Автор: Melina F.
Издательство: Книга по Требованию
Год:2010
Цена:
2783 руб
Нет в наличии
Поиск: The Impact of Multiplication Operators on the Ill-Posedness of Inverse Problems
НОВЫЙ ГОД СИМВОЛ 2013 ГОДАУКРАШЕНИЯ
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