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001 9910300137603321
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010   $a3-319-95264-1
024 7 $a10.1007/978-3-319-95264-2
035   $a(CKB)4100000006520002
035   $a(MiAaPQ)EBC5511126
035   $a(DE-He213)978-3-319-95264-2
035   $z(PPN)258847387
035   $a(PPN)230539092
035   $a(EXLCZ)994100000006520002
100   $a20180908d2018      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aVariational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization $eNew Results in Modern Theory of Inverse Problems and an Application in Laser Optics /$fby Jens Flemming
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2018.
215   $a1 online resource (180 pages)
225 1 $aFrontiers in Mathematics,$x1660-8046
311   $a3-319-95263-3 
327   $aInverse problems, ill-posedness, regularization -- Variational source conditions yield convergence rates -- Existence of variational source conditions -- What are quadratic inverse problems? -- Tikhonov regularization -- Regularization by decomposition -- Variational source conditions -- Aren?t all questions answered? -- Sparsity and 1-regularization -- Ill-posedness in the l1-setting -- Convergence rates.
330   $aThe book collects and contributes new results on the theory and practice of ill-posed inverse problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard settings but also in situations up to now not covered by the literature. Especially, ill-posedness of linear operators with uncomplemented null spaces is examined. Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate results. A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics. Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with sparsity enforcing penalty.
410  0$aFrontiers in Mathematics,$x1660-8046
606   $aNumerical analysis
606   $aOperator theory
606   $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050
606   $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139
615  0$aNumerical analysis.
615  0$aOperator theory.
615 14$aNumerical Analysis.
615 24$aOperator Theory.
676   $a515.357
700   $aFlemming$b Jens$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767935
906   $aBOOK
912   $a9910300137603321
996   $aVariational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization$91563829
997   $aUNINA