Inverse and ill-posed problems :: theory and applications /
The text demonstrates the methods for proving the existence (if et all) and finding of inverse and ill-posed problems solutions in linear algebra, integral and operator equations, integral geometry, spectral inverse problems, and inverse scattering problems. It is given comprehensive background mate...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin :
De Gruyter,
2011.
|
| Schriftenreihe: | Inverse and ill-posed problems series ;
v. 55. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The text demonstrates the methods for proving the existence (if et all) and finding of inverse and ill-posed problems solutions in linear algebra, integral and operator equations, integral geometry, spectral inverse problems, and inverse scattering problems. It is given comprehensive background material for linear ill-posed problems and for coefficient inverse problems for hyperbolic, parabolic, and elliptic equations. A lot of examples for inverse problems from physics, geophysics, biology, medicine, and other areas of application of mathematics are included. |
| Beschreibung: | 9.2 Formulation of the initial boundary value problem for the Laplace equation in the form of an inverse problem. Reduction to an operator equation. |
| Beschreibung: | 1 online resource (xv, 475 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9783110224016 3110224011 3110224003 9783110224009 |
Internformat
MARC
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| 100 | 1 | |a Kabanikhin, S. I. |0 http://id.loc.gov/authorities/names/n85010727 | |
| 245 | 1 | 0 | |a Inverse and ill-posed problems : |b theory and applications / |c Sergey I. Kabanikhin. |
| 260 | |a Berlin : |b De Gruyter, |c 2011. | ||
| 300 | |a 1 online resource (xv, 475 pages) : |b illustrations | ||
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| 490 | 1 | |a Inverse and ill-posed problems series ; |v 55 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Preface; Denotations; 1 Basic concepts and examples; 1.1 On the definition of inverse and ill-posed problems; 1.2 Examples of inverse and ill-posed problems; 2 Ill-posed problems; 2.1 Well-posed and ill-posed problems; 2.2 On stability in different spaces; 2.3 Quasi-solution. The Ivanov theorems; 2.4 The Lavrentiev method; 2.5 The Tikhonov regularization method; 2.6 Gradient methods; 2.7 An estimate of the convergence rate with respect to the objective functional; 2.8 Conditional stability estimate and strong convergence of gradient methods applied to ill-posed problems. | |
| 505 | 8 | |a 2.9 The pseudoinverse and the singular value decomposition of an operator3 Ill-posed problems of linear algebra; 3.1 Generalization of the concept of a solution. Pseudo-solutions; 3.2 Regularization method; 3.3 Criteria for choosing the regularization parameter; 3.4 Iterative regularization algorithms; 3.5 Singular value decomposition; 3.6 The singular value decomposition algorithm and the Godunov method; 3.7 The square root method; 3.8 Exercises; 4 Integral equations; 4.1 Fredholm integral equations of the first kind; 4.2 Regularization of linear Volterra integral equations of the first kind. | |
| 505 | 8 | |a 4.3 Volterra operator equations with boundedly Lipschitz-continuous kernel4.4 Local well-posedness and uniqueness on the whole; 4.5 Well-posedness in a neighborhood of the exact solution; 4.6 Regularization of nonlinear operator equations of the first kind; 5 Integral geometry; 5.1 The Radon problem; 5.2 Reconstructing a function from its spherical means; 5.3 Determining a function of a single variable from the values of its integrals. The problem of moments; 5.4 Inverse kinematic problem of seismology; 6 Inverse spectral and scattering problems. | |
| 505 | 8 | |a 6.1 Direct Sturm-Liouville problem on a finite interval6.2 Inverse Sturm-Liouville problems on a finite interval; 6.3 The Gelfand-Levitan method on a finite interval; 6.4 Inverse scattering problems; 6.5 Inverse scattering problems in the time domain; 7 Linear problems for hyperbolic equations; 7.1 Reconstruction of a function from its spherical means; 7.2 The Cauchy problem for a hyperbolic equation with data on a time-like surface; 7.3 The inverse thermoacoustic problem; 7.4 Linearized multidimensional inverse problem for the wave equation; 8 Linear problems for parabolic equations. | |
| 505 | 8 | |a 8.1 On the formulation of inverse problems for parabolic equations and their relationship with the corresponding inverse problems for hyperbolic equations8.2 Inverse problem of heat conduction with reverse time (retrospective inverse problem); 8.3 Inverse boundary-value problems and extension problems; 8.4 Interior problems and problems of determining sources; 9 Linear problems for elliptic equations; 9.1 The uniqueness theorem and a conditional stability estimate on a plane. | |
| 500 | |a 9.2 Formulation of the initial boundary value problem for the Laplace equation in the form of an inverse problem. Reduction to an operator equation. | ||
| 520 | |a The text demonstrates the methods for proving the existence (if et all) and finding of inverse and ill-posed problems solutions in linear algebra, integral and operator equations, integral geometry, spectral inverse problems, and inverse scattering problems. It is given comprehensive background material for linear ill-posed problems and for coefficient inverse problems for hyperbolic, parabolic, and elliptic equations. A lot of examples for inverse problems from physics, geophysics, biology, medicine, and other areas of application of mathematics are included. | ||
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Inverse problems (Differential equations) |0 http://id.loc.gov/authorities/subjects/sh85067684 | |
| 650 | 0 | |a Boundary value problems |x Improperly posed problems. |0 http://id.loc.gov/authorities/subjects/sh85016104 | |
| 650 | 6 | |a Problèmes inverses (Équations différentielles) | |
| 650 | 6 | |a Problèmes aux limites |x Problèmes mal posés. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x General. |2 bisacsh | |
| 650 | 7 | |a Boundary value problems |x Improperly posed problems |2 fast | |
| 650 | 7 | |a Inverse problems (Differential equations) |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Kabanikhin, S I. |t Inverse and Ill-posed Problems : Theory and Applications. |d Berlin : De Gruyter, ©2011 |z 9783110224009 |
| 830 | 0 | |a Inverse and ill-posed problems series ; |v v. 55. |0 http://id.loc.gov/authorities/names/no95046818 | |
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Datensatz im Suchindex
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| author | Kabanikhin, S. I. |
| author_GND | http://id.loc.gov/authorities/names/n85010727 |
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| contents | Preface; Denotations; 1 Basic concepts and examples; 1.1 On the definition of inverse and ill-posed problems; 1.2 Examples of inverse and ill-posed problems; 2 Ill-posed problems; 2.1 Well-posed and ill-posed problems; 2.2 On stability in different spaces; 2.3 Quasi-solution. The Ivanov theorems; 2.4 The Lavrentiev method; 2.5 The Tikhonov regularization method; 2.6 Gradient methods; 2.7 An estimate of the convergence rate with respect to the objective functional; 2.8 Conditional stability estimate and strong convergence of gradient methods applied to ill-posed problems. 2.9 The pseudoinverse and the singular value decomposition of an operator3 Ill-posed problems of linear algebra; 3.1 Generalization of the concept of a solution. Pseudo-solutions; 3.2 Regularization method; 3.3 Criteria for choosing the regularization parameter; 3.4 Iterative regularization algorithms; 3.5 Singular value decomposition; 3.6 The singular value decomposition algorithm and the Godunov method; 3.7 The square root method; 3.8 Exercises; 4 Integral equations; 4.1 Fredholm integral equations of the first kind; 4.2 Regularization of linear Volterra integral equations of the first kind. 4.3 Volterra operator equations with boundedly Lipschitz-continuous kernel4.4 Local well-posedness and uniqueness on the whole; 4.5 Well-posedness in a neighborhood of the exact solution; 4.6 Regularization of nonlinear operator equations of the first kind; 5 Integral geometry; 5.1 The Radon problem; 5.2 Reconstructing a function from its spherical means; 5.3 Determining a function of a single variable from the values of its integrals. The problem of moments; 5.4 Inverse kinematic problem of seismology; 6 Inverse spectral and scattering problems. 6.1 Direct Sturm-Liouville problem on a finite interval6.2 Inverse Sturm-Liouville problems on a finite interval; 6.3 The Gelfand-Levitan method on a finite interval; 6.4 Inverse scattering problems; 6.5 Inverse scattering problems in the time domain; 7 Linear problems for hyperbolic equations; 7.1 Reconstruction of a function from its spherical means; 7.2 The Cauchy problem for a hyperbolic equation with data on a time-like surface; 7.3 The inverse thermoacoustic problem; 7.4 Linearized multidimensional inverse problem for the wave equation; 8 Linear problems for parabolic equations. 8.1 On the formulation of inverse problems for parabolic equations and their relationship with the corresponding inverse problems for hyperbolic equations8.2 Inverse problem of heat conduction with reverse time (retrospective inverse problem); 8.3 Inverse boundary-value problems and extension problems; 8.4 Interior problems and problems of determining sources; 9 Linear problems for elliptic equations; 9.1 The uniqueness theorem and a conditional stability estimate on a plane. |
| ctrlnum | (OCoLC)772845127 |
| dewey-full | 515.357 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.357 |
| dewey-search | 515.357 |
| dewey-sort | 3515.357 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn772845127 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:11Z |
| institution | BVB |
| isbn | 9783110224016 3110224011 3110224003 9783110224009 |
| language | English |
| oclc_num | 772845127 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xv, 475 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | De Gruyter, |
| record_format | marc |
| series | Inverse and ill-posed problems series ; |
| series2 | Inverse and ill-posed problems series ; |
| spelling | Kabanikhin, S. I. http://id.loc.gov/authorities/names/n85010727 Inverse and ill-posed problems : theory and applications / Sergey I. Kabanikhin. Berlin : De Gruyter, 2011. 1 online resource (xv, 475 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file rda Inverse and ill-posed problems series ; 55 Includes bibliographical references and index. Preface; Denotations; 1 Basic concepts and examples; 1.1 On the definition of inverse and ill-posed problems; 1.2 Examples of inverse and ill-posed problems; 2 Ill-posed problems; 2.1 Well-posed and ill-posed problems; 2.2 On stability in different spaces; 2.3 Quasi-solution. The Ivanov theorems; 2.4 The Lavrentiev method; 2.5 The Tikhonov regularization method; 2.6 Gradient methods; 2.7 An estimate of the convergence rate with respect to the objective functional; 2.8 Conditional stability estimate and strong convergence of gradient methods applied to ill-posed problems. 2.9 The pseudoinverse and the singular value decomposition of an operator3 Ill-posed problems of linear algebra; 3.1 Generalization of the concept of a solution. Pseudo-solutions; 3.2 Regularization method; 3.3 Criteria for choosing the regularization parameter; 3.4 Iterative regularization algorithms; 3.5 Singular value decomposition; 3.6 The singular value decomposition algorithm and the Godunov method; 3.7 The square root method; 3.8 Exercises; 4 Integral equations; 4.1 Fredholm integral equations of the first kind; 4.2 Regularization of linear Volterra integral equations of the first kind. 4.3 Volterra operator equations with boundedly Lipschitz-continuous kernel4.4 Local well-posedness and uniqueness on the whole; 4.5 Well-posedness in a neighborhood of the exact solution; 4.6 Regularization of nonlinear operator equations of the first kind; 5 Integral geometry; 5.1 The Radon problem; 5.2 Reconstructing a function from its spherical means; 5.3 Determining a function of a single variable from the values of its integrals. The problem of moments; 5.4 Inverse kinematic problem of seismology; 6 Inverse spectral and scattering problems. 6.1 Direct Sturm-Liouville problem on a finite interval6.2 Inverse Sturm-Liouville problems on a finite interval; 6.3 The Gelfand-Levitan method on a finite interval; 6.4 Inverse scattering problems; 6.5 Inverse scattering problems in the time domain; 7 Linear problems for hyperbolic equations; 7.1 Reconstruction of a function from its spherical means; 7.2 The Cauchy problem for a hyperbolic equation with data on a time-like surface; 7.3 The inverse thermoacoustic problem; 7.4 Linearized multidimensional inverse problem for the wave equation; 8 Linear problems for parabolic equations. 8.1 On the formulation of inverse problems for parabolic equations and their relationship with the corresponding inverse problems for hyperbolic equations8.2 Inverse problem of heat conduction with reverse time (retrospective inverse problem); 8.3 Inverse boundary-value problems and extension problems; 8.4 Interior problems and problems of determining sources; 9 Linear problems for elliptic equations; 9.1 The uniqueness theorem and a conditional stability estimate on a plane. 9.2 Formulation of the initial boundary value problem for the Laplace equation in the form of an inverse problem. Reduction to an operator equation. The text demonstrates the methods for proving the existence (if et all) and finding of inverse and ill-posed problems solutions in linear algebra, integral and operator equations, integral geometry, spectral inverse problems, and inverse scattering problems. It is given comprehensive background material for linear ill-posed problems and for coefficient inverse problems for hyperbolic, parabolic, and elliptic equations. A lot of examples for inverse problems from physics, geophysics, biology, medicine, and other areas of application of mathematics are included. Print version record. Inverse problems (Differential equations) http://id.loc.gov/authorities/subjects/sh85067684 Boundary value problems Improperly posed problems. http://id.loc.gov/authorities/subjects/sh85016104 Problèmes inverses (Équations différentielles) Problèmes aux limites Problèmes mal posés. MATHEMATICS Differential Equations General. bisacsh Boundary value problems Improperly posed problems fast Inverse problems (Differential equations) fast Print version: Kabanikhin, S I. Inverse and Ill-posed Problems : Theory and Applications. Berlin : De Gruyter, ©2011 9783110224009 Inverse and ill-posed problems series ; v. 55. http://id.loc.gov/authorities/names/no95046818 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=430031 Volltext |
| spellingShingle | Kabanikhin, S. I. Inverse and ill-posed problems : theory and applications / Inverse and ill-posed problems series ; Preface; Denotations; 1 Basic concepts and examples; 1.1 On the definition of inverse and ill-posed problems; 1.2 Examples of inverse and ill-posed problems; 2 Ill-posed problems; 2.1 Well-posed and ill-posed problems; 2.2 On stability in different spaces; 2.3 Quasi-solution. The Ivanov theorems; 2.4 The Lavrentiev method; 2.5 The Tikhonov regularization method; 2.6 Gradient methods; 2.7 An estimate of the convergence rate with respect to the objective functional; 2.8 Conditional stability estimate and strong convergence of gradient methods applied to ill-posed problems. 2.9 The pseudoinverse and the singular value decomposition of an operator3 Ill-posed problems of linear algebra; 3.1 Generalization of the concept of a solution. Pseudo-solutions; 3.2 Regularization method; 3.3 Criteria for choosing the regularization parameter; 3.4 Iterative regularization algorithms; 3.5 Singular value decomposition; 3.6 The singular value decomposition algorithm and the Godunov method; 3.7 The square root method; 3.8 Exercises; 4 Integral equations; 4.1 Fredholm integral equations of the first kind; 4.2 Regularization of linear Volterra integral equations of the first kind. 4.3 Volterra operator equations with boundedly Lipschitz-continuous kernel4.4 Local well-posedness and uniqueness on the whole; 4.5 Well-posedness in a neighborhood of the exact solution; 4.6 Regularization of nonlinear operator equations of the first kind; 5 Integral geometry; 5.1 The Radon problem; 5.2 Reconstructing a function from its spherical means; 5.3 Determining a function of a single variable from the values of its integrals. The problem of moments; 5.4 Inverse kinematic problem of seismology; 6 Inverse spectral and scattering problems. 6.1 Direct Sturm-Liouville problem on a finite interval6.2 Inverse Sturm-Liouville problems on a finite interval; 6.3 The Gelfand-Levitan method on a finite interval; 6.4 Inverse scattering problems; 6.5 Inverse scattering problems in the time domain; 7 Linear problems for hyperbolic equations; 7.1 Reconstruction of a function from its spherical means; 7.2 The Cauchy problem for a hyperbolic equation with data on a time-like surface; 7.3 The inverse thermoacoustic problem; 7.4 Linearized multidimensional inverse problem for the wave equation; 8 Linear problems for parabolic equations. 8.1 On the formulation of inverse problems for parabolic equations and their relationship with the corresponding inverse problems for hyperbolic equations8.2 Inverse problem of heat conduction with reverse time (retrospective inverse problem); 8.3 Inverse boundary-value problems and extension problems; 8.4 Interior problems and problems of determining sources; 9 Linear problems for elliptic equations; 9.1 The uniqueness theorem and a conditional stability estimate on a plane. Inverse problems (Differential equations) http://id.loc.gov/authorities/subjects/sh85067684 Boundary value problems Improperly posed problems. http://id.loc.gov/authorities/subjects/sh85016104 Problèmes inverses (Équations différentielles) Problèmes aux limites Problèmes mal posés. MATHEMATICS Differential Equations General. bisacsh Boundary value problems Improperly posed problems fast Inverse problems (Differential equations) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85067684 http://id.loc.gov/authorities/subjects/sh85016104 |
| title | Inverse and ill-posed problems : theory and applications / |
| title_auth | Inverse and ill-posed problems : theory and applications / |
| title_exact_search | Inverse and ill-posed problems : theory and applications / |
| title_full | Inverse and ill-posed problems : theory and applications / Sergey I. Kabanikhin. |
| title_fullStr | Inverse and ill-posed problems : theory and applications / Sergey I. Kabanikhin. |
| title_full_unstemmed | Inverse and ill-posed problems : theory and applications / Sergey I. Kabanikhin. |
| title_short | Inverse and ill-posed problems : |
| title_sort | inverse and ill posed problems theory and applications |
| title_sub | theory and applications / |
| topic | Inverse problems (Differential equations) http://id.loc.gov/authorities/subjects/sh85067684 Boundary value problems Improperly posed problems. http://id.loc.gov/authorities/subjects/sh85016104 Problèmes inverses (Équations différentielles) Problèmes aux limites Problèmes mal posés. MATHEMATICS Differential Equations General. bisacsh Boundary value problems Improperly posed problems fast Inverse problems (Differential equations) fast |
| topic_facet | Inverse problems (Differential equations) Boundary value problems Improperly posed problems. Problèmes inverses (Équations différentielles) Problèmes aux limites Problèmes mal posés. MATHEMATICS Differential Equations General. Boundary value problems Improperly posed problems |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=430031 |
| work_keys_str_mv | AT kabanikhinsi inverseandillposedproblemstheoryandapplications |