Hidden Bibliographic Details
| ISBN: | 9783319952642
3319952641
9783319952635
3319952633
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| Notes: | Includes bibliographical references and index.
Online resource; title from PDF title page (SpringerLink, viewed September 17, 2018).
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| Summary: | The book collects and contributes new results on the theory and practice of ill-posed inverse problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard settings but also in situations up to now not covered by the literature. Especially, ill-posedness of linear operators with uncomplemented null spaces is examined. Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate results. A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics. Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with sparsity enforcing penalty.--
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| Other form: | Print version: Flemming, Jens. Variational source conditions, quadratic inverse problems, sparsity promoting regularization. Cham, Switzerland : Birkhäuser, 2018 3319952633 9783319952635
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