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...
Gespeichert in:
| Weitere Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston :
De Gruyter,
©2012.
|
| Schriftenreihe: | Radon series on computational and applied mathematics ;
10. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xi, 283 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 265-279) and index. |
| ISBN: | 9783110255720 3110255723 9783112204504 3112204506 1283627922 9781283627924 9786613940377 6613940372 |
| ISSN: | 1865-3707 ; |
Internformat
MARC
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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 | ||
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| 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. | ||
| 650 | 0 | |a Banach spaces. |0 http://id.loc.gov/authorities/subjects/sh85011441 | |
| 650 | 0 | |a Parameter estimation. |0 http://id.loc.gov/authorities/subjects/sh85097853 | |
| 650 | 0 | |a Differential equations, Partial. |0 http://id.loc.gov/authorities/subjects/sh85037912 | |
| 650 | 4 | |a Banach spaces. | |
| 650 | 4 | |a Iterative methods. | |
| 650 | 4 | |a Regularization theory. | |
| 650 | 4 | |a Tikhonov regularization. | |
| 650 | 6 | |a Espaces de Banach. | |
| 650 | 6 | |a Estimation d'un paramètre. | |
| 650 | 6 | |a Équations aux dérivées partielles. | |
| 650 | 7 | |a MATHEMATICS |x Transformations. |2 bisacsh | |
| 650 | 7 | |a Banach spaces |2 fast | |
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| 650 | 7 | |a Regularisierung |2 gnd |0 http://d-nb.info/gnd/4124043-1 | |
| 700 | 1 | |a Schuster, Thomas, |d 1971- |0 http://id.loc.gov/authorities/names/no2007069211 | |
| 776 | 0 | 8 | |i Print version: |z 9786613940377 |w (DLC) 2012013065 |
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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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Datensatz im Suchindex
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| author_facet | Schuster, Thomas, 1971- |
| author_sort | Schuster, Thomas, 1971- |
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| collection | ZDB-4-EBA |
| contents | 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. |
| ctrlnum | (OCoLC)812251485 |
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inverse.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="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.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">English.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Banach spaces.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85011441</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Parameter estimation.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85097853</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Differential equations, Partial.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85037912</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Banach spaces.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Iterative methods.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Regularization theory.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Tikhonov regularization.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Espaces de Banach.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Estimation d'un paramètre.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Équations aux dérivées partielles.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Transformations.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Banach spaces</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Differential equations, Partial</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Parameter estimation</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Banach-Raum</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4004402-6</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Regularisierung</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4124043-1</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Schuster, Thomas,</subfield><subfield code="d">1971-</subfield><subfield code="0">http://id.loc.gov/authorities/names/no2007069211</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="z">9786613940377</subfield><subfield code="w">(DLC) 2012013065</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Radon series on computational and applied mathematics ;</subfield><subfield code="v">10.</subfield><subfield code="0">http://id.loc.gov/authorities/names/no2008036485</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=494131</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="880" ind1="0" ind2=" "><subfield code="6">505-00/(S</subfield><subfield code="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. 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| id | ZDB-4-EBA-ocn812251485 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:24:59Z |
| institution | BVB |
| isbn | 9783110255720 3110255723 9783112204504 3112204506 1283627922 9781283627924 9786613940377 6613940372 |
| issn | 1865-3707 ; |
| language | English |
| oclc_num | 812251485 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xi, 283 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | De Gruyter, |
| record_format | marc |
| series | Radon series on computational and applied mathematics ; |
| series2 | Radon series on computational and applied mathematics, |
| spelling | Regularization methods in Banach spaces / by Thomas Schuster [and others]. Berlin ; Boston : De Gruyter, ©2012. 1 online resource (xi, 283 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Radon series on computational and applied mathematics, 1865-3707 ; 10 Includes bibliographical references (pages 265-279) and index. 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. Print version record. 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. English. Banach spaces. http://id.loc.gov/authorities/subjects/sh85011441 Parameter estimation. http://id.loc.gov/authorities/subjects/sh85097853 Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Banach spaces. Iterative methods. Regularization theory. Tikhonov regularization. Espaces de Banach. Estimation d'un paramètre. Équations aux dérivées partielles. MATHEMATICS Transformations. bisacsh Banach spaces fast Differential equations, Partial fast Parameter estimation fast Banach-Raum gnd http://d-nb.info/gnd/4004402-6 Regularisierung gnd http://d-nb.info/gnd/4124043-1 Schuster, Thomas, 1971- http://id.loc.gov/authorities/names/no2007069211 Print version: 9786613940377 (DLC) 2012013065 Radon series on computational and applied mathematics ; 10. http://id.loc.gov/authorities/names/no2008036485 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=494131 Volltext 505-00/(S 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. |
| spellingShingle | Regularization methods in Banach spaces / Radon series on computational and applied mathematics ; 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. Banach spaces. http://id.loc.gov/authorities/subjects/sh85011441 Parameter estimation. http://id.loc.gov/authorities/subjects/sh85097853 Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Banach spaces. Iterative methods. Regularization theory. Tikhonov regularization. Espaces de Banach. Estimation d'un paramètre. Équations aux dérivées partielles. MATHEMATICS Transformations. bisacsh Banach spaces fast Differential equations, Partial fast Parameter estimation fast Banach-Raum gnd http://d-nb.info/gnd/4004402-6 Regularisierung gnd http://d-nb.info/gnd/4124043-1 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85011441 http://id.loc.gov/authorities/subjects/sh85097853 http://id.loc.gov/authorities/subjects/sh85037912 http://d-nb.info/gnd/4004402-6 http://d-nb.info/gnd/4124043-1 |
| title | Regularization methods in Banach spaces / |
| title_auth | Regularization methods in Banach spaces / |
| title_exact_search | Regularization methods in Banach spaces / |
| title_full | Regularization methods in Banach spaces / by Thomas Schuster [and others]. |
| title_fullStr | Regularization methods in Banach spaces / by Thomas Schuster [and others]. |
| title_full_unstemmed | Regularization methods in Banach spaces / by Thomas Schuster [and others]. |
| title_short | Regularization methods in Banach spaces / |
| title_sort | regularization methods in banach spaces |
| topic | Banach spaces. http://id.loc.gov/authorities/subjects/sh85011441 Parameter estimation. http://id.loc.gov/authorities/subjects/sh85097853 Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Banach spaces. Iterative methods. Regularization theory. Tikhonov regularization. Espaces de Banach. Estimation d'un paramètre. Équations aux dérivées partielles. MATHEMATICS Transformations. bisacsh Banach spaces fast Differential equations, Partial fast Parameter estimation fast Banach-Raum gnd http://d-nb.info/gnd/4004402-6 Regularisierung gnd http://d-nb.info/gnd/4124043-1 |
| topic_facet | Banach spaces. Parameter estimation. Differential equations, Partial. Iterative methods. Regularization theory. Tikhonov regularization. Espaces de Banach. Estimation d'un paramètre. Équations aux dérivées partielles. MATHEMATICS Transformations. Banach spaces Differential equations, Partial Parameter estimation Banach-Raum Regularisierung |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=494131 |
| work_keys_str_mv | AT schusterthomas regularizationmethodsinbanachspaces |