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  • 1
    Buch
    Buch
    Berlin [u.a.] :De Gruyter,
    UID:
    almafu_BV040424773
    Umfang: XI, 283 S. : , graph. Darst. ; , 25 cm.
    ISBN: 3-11-025524-3 , 978-3-11-025524-9
    Serie: Radon series on computational and applied mathematics 10
    Anmerkung: Literatur-Verz.: S. 265 - 279
    Weitere Ausg.: Erscheint auch als Online-Ausgabe ISBN 978-3-11-025572-0
    Sprache: Englisch
    Fachgebiete: Mathematik
    RVK:
    Schlagwort(e): Regularisierung ; Banach-Raum
    Mehr zum Autor: Schuster, Thomas 1971-
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
  • 2
    Online-Ressource
    Online-Ressource
    Berlin ;Boston :De Gruyter,
    UID:
    almafu_9958353803302883
    Umfang: 1 online resource (294p.)
    ISBN: 9783110255720
    Serie: Radon Series on Computational and Applied Mathematics ; 10
    Inhalt: Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.
    Anmerkung: Frontmatter -- , Preface -- , Contents -- , Part I. Why to use Banach spaces in regularization theory? -- , Part II. Geometry and mathematical tools of Banach spaces -- , Part III. Tikhonov-type regularization -- , Part IV. Iterative regularization -- , Part V. The method of approximate inverse -- , Bibliography -- , Index , In English.
    Weitere Ausg.: ISBN 978-3-11-025524-9
    Sprache: Englisch
    Fachgebiete: Mathematik
    RVK:
    URL: Cover
    URL: Cover
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
  • 3
    UID:
    gbv_1655759663
    Umfang: Online-Ressource
    Ausgabe: 1. Aufl.
    Ausgabe: 2011
    ISBN: 3110255723
    Serie: Radon Series on Computational and Applied Mathematics 10
    Inhalt: 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. Thomas Schuster, Carl von Ossietzky Universität Oldenburg, Germany;Barbara Kaltenbacher, University of Stuttgart, Germany; Bernd Hofmann, Chemnitz University of Technology, Germany; Kamil S. Kazimierski, University of Bremen, Germany.
    Anmerkung: In English
    Weitere Ausg.: ISBN 3110255243
    Weitere Ausg.: ISBN 9781283627924
    Weitere Ausg.: ISBN 9783110255249
    Weitere Ausg.: ISBN 9783112204504
    Weitere Ausg.: Erscheint auch als Druck-Ausgabe
    Weitere Ausg.: Erscheint auch als Druck-Ausgabe ISBN 978-1-283-62792-4
    Weitere Ausg.: Erscheint auch als Druck-Ausgabe Regularization methods in Banach spaces Berlin [u.a.] : De Gruyter, 2012 ISBN 3110255243
    Weitere Ausg.: ISBN 9783110255249
    Weitere Ausg.: Erscheint auch als Druck-Ausgabe ISBN 978-3-11-220450-4
    Sprache: Englisch
    Fachgebiete: Mathematik
    RVK:
    RVK:
    Schlagwort(e): Regularisierung ; Banach-Raum
    URL: Volltext  (lizenzpflichtig)
    URL: Cover
    URL: Cover
    Mehr zum Autor: Schuster, Thomas 1971-
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
  • 4
    Buch
    Buch
    Berlin [u.a.] : Walter de Gruyter GmbH & Co. KG
    UID:
    kobvindex_ZLB15519204
    Umfang: XI, 283 Seiten , graph. Darst. , 25 cm
    ISBN: 9783110255249 , 3110255243
    Serie: Radon series on computational and applied mathematics 10
    Anmerkung: Literaturangaben
    Sprache: Englisch
    Schlagwort(e): Regularisierung ; Banach-Raum
    Mehr zum Autor: Schuster, Thomas
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
  • 5
    Buch
    Buch
    Berlin [u.a.] : De Gruyter
    UID:
    b3kat_BV040424773
    Umfang: XI, 283 S. , graph. Darst. , 25 cm
    ISBN: 3110255243 , 9783110255249
    Serie: Radon series on computational and applied mathematics 10
    Anmerkung: Literatur-Verz.: S. 265 - 279
    Weitere Ausg.: Erscheint auch als Online-Ausgabe ISBN 978-3-11-025572-0
    Sprache: Englisch
    Fachgebiete: Mathematik
    RVK:
    Schlagwort(e): Regularisierung ; Banach-Raum
    Mehr zum Autor: Schuster, Thomas 1971-
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
  • 6
    Online-Ressource
    Online-Ressource
    Berlin ;Boston :De Gruyter,
    UID:
    edocfu_9958353803302883
    Umfang: 1 online resource (294p.)
    ISBN: 9783110255720
    Serie: Radon Series on Computational and Applied Mathematics ; 10
    Inhalt: Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.
    Anmerkung: Frontmatter -- , Preface -- , Contents -- , Part I. Why to use Banach spaces in regularization theory? -- , Part II. Geometry and mathematical tools of Banach spaces -- , Part III. Tikhonov-type regularization -- , Part IV. Iterative regularization -- , Part V. The method of approximate inverse -- , Bibliography -- , Index , In English.
    Weitere Ausg.: ISBN 978-3-11-025524-9
    Sprache: Englisch
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
  • 7
    UID:
    edocfu_9959242397902883
    Umfang: 1 online resource (296 p.)
    Ausgabe: 1st ed.
    ISBN: 3-11-025572-3 , 1-283-62792-2 , 9786613940377
    Serie: Radon series on computational and applied mathematics, 10
    Inhalt: Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.
    Anmerkung: Description based upon print version of record. , Front matter -- , Preface -- , Contents -- , Part I. Why to use Banach spaces in regularization theory? -- , Part II. Geometry and mathematical tools of Banach spaces -- , Part III. Tikhonov-type regularization -- , Part IV. Iterative regularization -- , Part V. The method of approximate inverse -- , Bibliography -- , Index , Issued also in print. , English
    Weitere Ausg.: ISBN 3-11-220450-6
    Weitere Ausg.: ISBN 3-11-025524-3
    Sprache: Englisch
    Fachgebiete: Mathematik
    RVK:
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
  • 8
    UID:
    almafu_9959242397902883
    Umfang: 1 online resource (296 p.)
    Ausgabe: 1st ed.
    ISBN: 3-11-025572-3 , 1-283-62792-2 , 9786613940377
    Serie: Radon series on computational and applied mathematics, 10
    Inhalt: Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.
    Anmerkung: Description based upon print version of record. , Front matter -- , Preface -- , Contents -- , Part I. Why to use Banach spaces in regularization theory? -- , Part II. Geometry and mathematical tools of Banach spaces -- , Part III. Tikhonov-type regularization -- , Part IV. Iterative regularization -- , Part V. The method of approximate inverse -- , Bibliography -- , Index , Issued also in print. , English
    Weitere Ausg.: ISBN 3-11-220450-6
    Weitere Ausg.: ISBN 3-11-025524-3
    Sprache: Englisch
    Fachgebiete: Mathematik
    RVK:
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
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