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|a Variational source conditions, quadratic inverse problems, sparsity promoting regularization
|b new results in modern theory of inverse problems and an application in laser optics
|c Jens Flemming
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|a 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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SOLR
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1792254459998371840 |
access_facet |
Local Holdings |
author |
Flemming, Jens |
author_facet |
Flemming, Jens |
author_role |
aut |
author_sort |
Flemming, Jens 1985- |
author_variant |
j f jf |
barcode |
(DE-Ch1)000000312706 |
barcode_dech1 |
000000312706 |
building |
(DE-Ch1)UB |
callnumber-first |
Q - Science |
callnumber-label |
QA371 |
callnumber-raw |
QA371 |
callnumber-search |
QA371 |
callnumber-sort |
QA 3371 |
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QA - Mathematics |
callnumber_dech1 |
SA 2017 fle, 1033161 |
collcode_dech1 |
Freihand |
contents |
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.-- |
ctrlnum |
(DE-627)1644329638, (DE-576)513707751, (DE-599)BSZ513707751, (OCoLC)1077717042 |
dech1_date |
2019-02-28T11:48:34Z |
doi_str_mv |
10.1007/978-3-319-95264-2 |
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Local |
facet_local_del330 |
Inkorrekt gestelltes Problem |
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Mathematik |
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science-mathematics |
footnote |
Includes bibliographical references and index |
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Book, Thesis |
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Thesis |
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Book, E-Book |
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Book, E-Book |
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Buch |
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text-print-monograph-independent-thesis |
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e-Book |
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Book |
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Book, E-Book |
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Thesis |
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Hochschulschrift (DE-588)4113937-9 (DE-627)105825778 (DE-576)209480580 gnd-content |
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Hochschulschrift |
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not assigned |
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Germany |
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0-1644329638 |
illustrated |
Not Illustrated |
imprint |
Cham, Switzerland, Birkhäuser, [2018] |
imprint_str_mv |
Cham, Switzerland: Birkhäuser, [2018] |
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DE-Ch1 |
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3319952633, 9783319952635 |
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English |
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2024-02-29T17:17:25.267Z |
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MATHEMATICS / Calculus, MATHEMATICS / Mathematical Analysis, Functional analysis & transforms, Numerical analysis, Inverse problems (Differential equations), Inkorrekt gestelltes Problem |
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10.1007/978-3-319-95264-2 |
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(DE-588)1020883472, (DE-627)69139105X, (DE-576)352513926 |
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xi, 182 Seiten; Illustrationen; 24 cm |
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Cham, Switzerland |
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Birkhäuser |
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Frontiers in mathematics |
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(DE-Ch1)SA 2017 fle, (DE-Ch1)1033161 |
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0 |
spelling |
Flemming, Jens 1985- VerfasserIn (DE-588)1020883472 (DE-627)69139105X (DE-576)352513926 aut, Variational source conditions, quadratic inverse problems, sparsity promoting regularization new results in modern theory of inverse problems and an application in laser optics Jens Flemming, Cham, Switzerland Birkhäuser [2018], xi, 182 Seiten Illustrationen 24 cm, Text txt rdacontent, ohne Hilfsmittel zu benutzen n rdamedia, Band nc rdacarrier, Frontiers in mathematics, Includes bibliographical references and index, Habilitationsschrift Technische Universität Chemnitz 2018, 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.--, MATHEMATICS / Calculus, MATHEMATICS / Mathematical Analysis, Functional analysis & transforms, Numerical analysis, Inverse problems (Differential equations), Hochschulschrift (DE-588)4113937-9 (DE-627)105825778 (DE-576)209480580 gnd-content, s (DE-588)4186951-5 (DE-627)105275743 (DE-576)210042613 Inkorrekt gestelltes Problem gnd, (DE-627), 9783319952642, Erscheint auch als Online-Ausgabe Flemming, Jens Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization Cham : Springer International Publishing, 2018 Online-Ressource (XI, 182 p. 35 illus, online resource) (DE-627)1031840001 (DE-576)511571402 9783319952642, https://www.gbv.de/dms/tib-ub-hannover/1644329638.pdf V:DE-601 B:DE-89 pdf/application Inhaltsverzeichnis, DE-Ch1 epn:3310767809 2019-02-28T11:48:34Z |
spellingShingle |
Flemming, Jens, Variational source conditions, quadratic inverse problems, sparsity promoting regularization: new results in modern theory of inverse problems and an application in laser optics, 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.--, MATHEMATICS / Calculus, MATHEMATICS / Mathematical Analysis, Functional analysis & transforms, Numerical analysis, Inverse problems (Differential equations), Hochschulschrift, Inkorrekt gestelltes Problem |
swb_id_str |
513707751 |
title |
Variational source conditions, quadratic inverse problems, sparsity promoting regularization: new results in modern theory of inverse problems and an application in laser optics |
title_auth |
Variational source conditions, quadratic inverse problems, sparsity promoting regularization new results in modern theory of inverse problems and an application in laser optics |
title_full |
Variational source conditions, quadratic inverse problems, sparsity promoting regularization new results in modern theory of inverse problems and an application in laser optics Jens Flemming |
title_fullStr |
Variational source conditions, quadratic inverse problems, sparsity promoting regularization new results in modern theory of inverse problems and an application in laser optics Jens Flemming |
title_full_unstemmed |
Variational source conditions, quadratic inverse problems, sparsity promoting regularization new results in modern theory of inverse problems and an application in laser optics Jens Flemming |
title_short |
Variational source conditions, quadratic inverse problems, sparsity promoting regularization |
title_sort |
variational source conditions quadratic inverse problems sparsity promoting regularization new results in modern theory of inverse problems and an application in laser optics |
title_sub |
new results in modern theory of inverse problems and an application in laser optics |
title_unstemmed |
Variational source conditions, quadratic inverse problems, sparsity promoting regularization: new results in modern theory of inverse problems and an application in laser optics |
topic |
MATHEMATICS / Calculus, MATHEMATICS / Mathematical Analysis, Functional analysis & transforms, Numerical analysis, Inverse problems (Differential equations), Hochschulschrift, Inkorrekt gestelltes Problem |
topic_facet |
MATHEMATICS / Calculus, MATHEMATICS / Mathematical Analysis, Functional analysis & transforms, Numerical analysis, Inverse problems (Differential equations), Hochschulschrift, Inkorrekt gestelltes Problem |
url |
https://www.gbv.de/dms/tib-ub-hannover/1644329638.pdf |