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  • 1
    Online Resource
    Online Resource
    Iterative methods for ill-posed problems : an introduction (2011)
    Berlin : De Gruyter
    Details
    UID:
    gbv_1655720163
    Format: 1 Online-Ressource (XI, 136 Seiten) , Diagramme
    ISBN: 9783110250657
    Series Statement: Inverse and Ill-Posed Problems Series 54
    Content: Ill-posed problemsare encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations.These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus o
    Note: In English
    Additional Edition: ISBN 9783110250640
    Additional Edition: Erscheint auch als Druck-Ausgabe Bakušinskij, Anatolij B. Iterative methods for ill-posed problems Berlin [u.a.] : De Gruyter, 2011 ISBN 3110250640
    Additional Edition: ISBN 9783110250640
    Language: English
    Subjects: Mathematics
    RVK:
    SK 620
    RVK:
    SK 920
    RVK:
    SK 910
    Keywords: Inkorrekt gestelltes Problem ; Iteration ; Operatorgleichung ; Hilbert-Raum
    DOI: 10.1515/9783110250657
    URL: Volltext  (lizenzpflichtig)
    URL: lizenzpflichtig
    URL: Cover
    URL: Inhaltstext
    URL: Cover
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  • 2
    Book
    Book
    Iterative methods for ill-posed problems : an introduction (2011)
    Berlin [u.a.] : Walter de Gruyter GmbH & Co. KG
    Details
    UID:
    kobvindex_ZLB15250692
    Format: XI, 136 Seiten , graph. Darst.
    ISBN: 9783110250640
    Series Statement: Inverse and ill-posed problems series 54
    Note: Literaturangaben , Text engl.
    Language: English
    Keywords: Inkorrekt gestelltes Problem ; Iteration ; Operatorgleichung ; Hilbert-Raum
    URL: http://d-nb.info/1009312847/04
    URL: http://deposit.d-nb.de/cgi-bin/dokserv?id=3645007&prov=M&dok_var=1&dok_ext=htm
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  • 3
    Book
    Book
    Iterative methods for ill-posed problems : an introduction (2011)
    Berlin [u.a.] : De Gruyter
    Details
    UID:
    gbv_63621866X
    Format: XI, 136 S. , Ill., graph. Darst. , 25 cm
    ISBN: 3110250640 , 9783110250640
    Series Statement: Inverse and ill-posed problems series 54
    Uniform Title: Iterativnye metody rešenija nekorrektnych zadač 〈engl.〉
    Note: Orig.-Ausg. ersch.: Moskva : Nauka, 1989 , Literaturverz. S. [132] - 136 , Machine generated contents note:1.The regularity condition. Newton's method -- 1.1.Preliminary results -- 1.2.Linearization procedure -- 1.3.Error analysis -- Problems -- 2.The Gauss -- Newton method -- 2.1.Motivation -- 2.2.Convergence rates -- Problems -- 3.The gradient method -- 3.1.The gradient method for regular problems -- 3.2.Ill-posed case -- Problems -- 4.Tikhonov's scheme -- 4.1.The Tikhonov functional -- 4.2.Properties of a minimizing sequence -- 4.3.Other types of convergence -- 4.4.Equations with noisy data -- Problems -- 5.Tikhonov's scheme for linear equations -- 5.1.The main convergence result -- 5.2.Elements of spectral theory -- 5.3.Minimizing sequences for linear equations , 5.4.A priori agreement between the regularization parameter and the error for equations with perturbed right-hand sides -- 5.5.The discrepancy principle -- 5.6.Approximation of a quasi-solution -- Problems -- 6.The gradient scheme for linear equations -- 6.1.The technique of spectral analysis -- 6.2.A priori stopping rule -- 6.3.A posteriori stopping rule -- Problems -- 7.Convergence rates for the approximation methods in the case of linear irregular equations -- 7.1.The source-type condition (STC) -- 7.2.STC for the gradient method -- 7.3.The saturation phenomena -- 7.4.Approximations in case of a perturbed STC -- 7.5.Accuracy of the estimates -- Problems -- 8.Equations with a convex discrepancy functional by Tikhonov's method -- 8.1.Some difficulties associated with Tikhonov's method in case of a convex discrepancy functional , 8.2.An illustrative example -- Problems -- 9.Iterative regularization principle -- 9.1.The idea of iterative regularization -- 9.2.The iteratively regularized gradient method -- Problems -- 10.The iteratively regularized Gauss -- Newton method -- 10.1.Convergence analysis -- 10.2.Further properties of IRGN iterations -- 10.3.A unified approach to the construction of iterative methods for irregular equations -- 10.4.The reverse connection control -- Problems -- 11.The stable gradient method for irregular nonlinear equations -- 11.1.Solving an auxiliary finite dimensional problem by the gradient descent method -- 11.2.Investigation of a difference inequality -- 11.3.The case of noisy data -- Problems -- 12.Relative computational efficiency of iteratively regularized methods -- 12.1.Generalized Gauss -- Newton methods -- 12.2.A more restrictive source condition , 12.3.Comparison to iteratively regularized gradient scheme -- Problems -- 13.Numerical investigation of two-dimensional inverse gravimetry problem -- 13.1.Problem formulation -- 13.2.The algorithm -- 13.3.Simulations -- Problems -- 14.Iteratively regularized methods for inverse problem in optical tomography -- 14.1.Statement of the problem -- 14.2.Simple example -- 14.3.Forward simulation -- 14.4.The inverse problem -- 14.5.Numerical results -- Problems -- 15.Feigenbaum's universality equation -- 15.1.The universal constants -- 15.2.Ill-posedness -- 15.3.Numerical algorithm for 2 ≤ z ≤ 12 -- 15.4.Regularized method for z ≥ 13 -- Problems -- 16.Conclusion. , Aus dem Russ. übers.
    Additional Edition: ISBN 9783110250657
    Additional Edition: Online-Ausg. Bakušinskij, Anatolij Borisovič, 1937 - Iterative methods for ill-posed problems Berlin : De Gruyter, 2011 ISBN 9783110250657
    Additional Edition: Erscheint auch als Online-Ausgabe Bakushinsky, Anatoly B Iterative Methods for Ill-Posed Problems - An Introduction Berlin/Boston : De Gruyter, Inc., 2010 ISBN 9783110250657
    Language: English
    Subjects: Mathematics
    RVK:
    SK 620
    RVK:
    SK 910
    RVK:
    SK 920
    Keywords: Inkorrekt gestelltes Problem ; Iteration ; Operatorgleichung ; Hilbert-Raum
    URL: Inhaltsverzeichnis
    URL: Ausführliche Beschreibung
    URL: Inhaltstext
    URL: Rezension
    URL: Inhaltsverzeichnis
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  • 4
    Online Resource
    Online Resource
    Iterative methods for ill-posed problems : an introduction (2011)
    Berlin [u.a.] :De Gruyter,
    Details
    UID:
    edocfu_BV042348150
    Format: 1 Online-Ressource (XI, 136 S.).
    ISBN: 1-283-16637-2 , 978-1-283-16637-9 , 978-3-11-025065-7
    Series Statement: Inverse and ill-posed problems series 54
    Uniform Title: Iterativnye metody resenija nekorrektnych zadač
    Note: Includes bibliographical references and index
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-11-025064-0
    Language: English
    Subjects: Mathematics
    RVK:
    SK 620
    RVK:
    SK 910
    RVK:
    SK 920
    Keywords: Inkorrekt gestelltes Problem ; Iteration ; Operatorgleichung ; Hilbert-Raum
    DOI: 10.1515/9783110250657
    URL: Volltext
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  • 5
    Online Resource
    Online Resource
    Iterative methods for ill-posed problems : an introduction (2011)
    Berlin ; : De Gruyter,
    Details
    UID:
    edocfu_9959235963402883
    Format: 1 online resource (152 p.)
    Edition: 1st ed.
    ISBN: 1-283-16637-2 , 9786613166371 , 3-11-025065-9
    Series Statement: Inverse and ill-posed problems series, 54
    Uniform Title: Iterativnye metody reshenii͡a nekorrektnykh zadach.
    Content: Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.
    Note: Description based upon print version of record. , Frontmatter -- , Preface -- , Contents -- , 1 The regularity condition. Newton's method -- , 2 The Gauss-Newton method -- , 3 The gradient method -- , 4 Tikhonov's scheme -- , 5 Tikhonov's scheme for linear equations -- , 6 The gradient scheme for linear equations -- , 7 Convergence rates for the approximation methods in the case of linear irregular equations -- , 8 Equations with a convex discrepancy functional by Tikhonov's method -- , 9 Iterative regularization principle -- , 10 The iteratively regularized Gauss-Newton method -- , 11 The stable gradient method for irregular nonlinear equations -- , 12 Relative computational efficiency of iteratively regularized methods -- , 13 Numerical investigation of two-dimensional inverse gravimetry problem -- , 14 Iteratively regularized methods for inverse problem in optical tomography -- , 15 Feigenbaum's universality equation -- , 16 Conclusion -- , References -- , Index , Issued also in print. , English
    Additional Edition: ISBN 3-11-025064-0
    Language: English
    DOI: 10.1515/9783110250657
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  • 6
    Online Resource
    Online Resource
    Iterative Methods for Ill-Posed Problems : An Introduction (2010)
    Berlin ; : De Gruyter,
    Details
    UID:
    almahu_9949462114202882
    Format: 1 online resource (136 p.)
    ISBN: 9783110250657 , 9783110238570
    Series Statement: Inverse and Ill-Posed Problems Series , 54
    Content: Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.
    Note: Frontmatter -- , Preface -- , Contents -- , 1 The regularity condition. Newton's method -- , 2 The Gauss-Newton method -- , 3 The gradient method -- , 4 Tikhonov's scheme -- , 5 Tikhonov's scheme for linear equations -- , 6 The gradient scheme for linear equations -- , 7 Convergence rates for the approximation methods in the case of linear irregular equations -- , 8 Equations with a convex discrepancy functional by Tikhonov's method -- , 9 Iterative regularization principle -- , 10 The iteratively regularized Gauss-Newton method -- , 11 The stable gradient method for irregular nonlinear equations -- , 12 Relative computational efficiency of iteratively regularized methods -- , 13 Numerical investigation of two-dimensional inverse gravimetry problem -- , 14 Iteratively regularized methods for inverse problem in optical tomography -- , 15 Feigenbaum's universality equation -- , 16 Conclusion -- , References -- , Index , Issued also in print. , Mode of access: Internet via World Wide Web. , In English.
    In: DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
    In: DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
    In: DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
    In: E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2010, De Gruyter, 9783110233544
    In: E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2010, De Gruyter, 9783110233551
    In: E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2010, De Gruyter, 9783110233636
    Additional Edition: ISBN 9783110250640
    Language: English
    Subjects: Mathematics
    RVK:
    SK 620
    DOI: 10.1515/9783110250657
    URL: https://doi.org/10.1515/9783110250657
    URL: https://www.degruyter.com/isbn/9783110250657
    URL: Cover
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  • 7
    Online Resource
    Online Resource
    Iterative methods for ill-posed problems : an introduction (2011)
    Berlin [u.a.] :De Gruyter,
    Details
    UID:
    almafu_BV042348150
    Format: 1 Online-Ressource (XI, 136 S.).
    ISBN: 1-283-16637-2 , 978-1-283-16637-9 , 978-3-11-025065-7
    Series Statement: Inverse and ill-posed problems series 54
    Uniform Title: Iterativnye metody resenija nekorrektnych zadač
    Note: Includes bibliographical references and index
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-11-025064-0
    Language: English
    Subjects: Mathematics
    RVK:
    SK 620
    RVK:
    SK 910
    RVK:
    SK 920
    Keywords: Inkorrekt gestelltes Problem ; Iteration ; Operatorgleichung ; Hilbert-Raum
    DOI: 10.1515/9783110250657
    URL: Volltext
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
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