Regularization methods in Banach spaces /

Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the associated forward operator acts between Hilbert s...

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Bibliographic Details
Other Authors: Schuster, Thomas, 1971-
Format: eBook
Language:English
Published: Berlin ; Boston : De Gruyter, ©2012.
Series:Radon series on computational and applied mathematics ; 10.
Subjects:
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245 0 0 |a Regularization methods in Banach spaces /  |c by Thomas Schuster [and others]. 
260 |a Berlin ;  |a Boston :  |b De Gruyter,  |c ©2012. 
300 |a 1 online resource (xi, 283 pages) :  |b illustrations 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a Radon series on computational and applied mathematics,  |x 1865-3707 ;  |v 10 
504 |a Includes bibliographical references (pages 265-279) and index. 
505 0 |a Why to use Banach spaces in regularization theory? -- Geometry and mathematical tools of Banach spaces -- Tikhonov-type regularization -- Iterative regularization -- The method of approximate inverse. 
588 0 |a Print version record. 
520 |a Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the associated forward operator acts between Hilbert spaces. However, for numerous problems the reasons for using a Hilbert space setting seem to be based rather on conventions than on an approprimate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, sparsity constraints using general Lp-norms or the BV-norm have recently become very popular. Meanwhile the most well-known methods have been investigated for linear and nonlinear operator equations in Banach spaces. Motivated by these facts the authors aim at collecting and publishing these results in a monograph. 
546 |a English. 
590 |a EBSCO eBook Academic Comprehensive Collection North America 
650 0 |a Banach spaces. 
650 0 |a Parameter estimation. 
650 0 |a Differential equations, Partial. 
700 1 |a Schuster, Thomas,  |d 1971- 
730 0 |a WORLDSHARE SUB RECORDS 
776 0 8 |i Print version:  |z 9786613940377  |w (DLC) 2012013065 
830 0 |a Radon series on computational and applied mathematics ;  |v 10. 
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880 0 |6 505-00/(S  |a Contents note continued: 7.2.2. Convergence rates for the iteratively regularized Landweber iteration with a priori stopping rule -- 7.3. The iteratively regularized Gauss-Newton method -- 7.3.1. Convergence with a priori parameter choice -- 7.3.2. Convergence with a posteriori parameter choice -- 7.3.3. Numerical illustration -- V. The method of approximate inverse -- 8. Setting of the method -- 9. Convergence analysis in Lp(Ω) and C(K) -- 9.1. The case X = Lp(Ω) -- 9.2. The case X = C(K) -- 9.3. An application to X-ray diffractometry -- 10.A glimpse of semi-discrete operator equations. 
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