Inverse and ill-posed problems: theory and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
2011
|
| Schriftenreihe: | Inverse and ill-posed problems series
v. 55 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| 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 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 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: | 1 Online-Ressource (xv, 475 pages) |
| ISBN: | 3110224011 9783110224016 |
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| 100 | 1 | |a Kabanikhin, S. I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Inverse and ill-posed problems |b theory and applications |c Sergey I. Kabanikhin |
| 264 | 1 | |a Berlin |b De Gruyter |c 2011 | |
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| 490 | 0 | |a Inverse and ill-posed problems series |v v. 55 | |
| 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 | ||
| 500 | |a Includes bibliographical references and index | ||
| 500 | |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 | ||
| 500 | |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 | ||
| 500 | |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 | ||
| 500 | |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 | ||
| 500 | |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 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 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 7 | |a MATHEMATICS / Differential Equations / General |2 bisacsh | |
| 650 | 7 | |a Boundary value problems / Improperly posed problems |2 fast | |
| 650 | 7 | |a Inverse problems (Differential equations) |2 fast | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Inverse problems (Differential equations) | |
| 650 | 4 | |a Boundary value problems |x Improperly posed problems | |
| 650 | 0 | 7 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Inverses Problem |0 (DE-588)4125161-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Inverses Problem |0 (DE-588)4125161-1 |D s |
| 689 | 0 | 1 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |D s |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Kabanikhin, S. I. |
| author_facet | Kabanikhin, S. I. |
| author_role | aut |
| author_sort | Kabanikhin, S. I. |
| author_variant | s i k si sik |
| building | Verbundindex |
| bvnumber | BV043075759 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)772845127 (DE-599)BVBBV043075759 |
| dewey-full | 515.357 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| 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 | DE-604.BV043075759 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:41Z |
| institution | BVB |
| isbn | 3110224011 9783110224016 |
| language | English |
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| physical | 1 Online-Ressource (xv, 475 pages) |
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| publishDate | 2011 |
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| series2 | Inverse and ill-posed problems series |
| spelling | Kabanikhin, S. I. Verfasser aut Inverse and ill-posed problems theory and applications Sergey I. Kabanikhin Berlin De Gruyter 2011 1 Online-Ressource (xv, 475 pages) txt rdacontent c rdamedia cr rdacarrier Inverse and ill-posed problems series v. 55 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 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 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 Mathematics MATHEMATICS / Differential Equations / General bisacsh Boundary value problems / Improperly posed problems fast Inverse problems (Differential equations) fast Mathematik Inverse problems (Differential equations) Boundary value problems Improperly posed problems Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Inverses Problem (DE-588)4125161-1 s Inkorrekt gestelltes Problem (DE-588)4186951-5 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=430031 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kabanikhin, S. I. Inverse and ill-posed problems theory and applications Mathematics MATHEMATICS / Differential Equations / General bisacsh Boundary value problems / Improperly posed problems fast Inverse problems (Differential equations) fast Mathematik Inverse problems (Differential equations) Boundary value problems Improperly posed problems Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4186951-5 (DE-588)4125161-1 |
| 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 | Mathematics MATHEMATICS / Differential Equations / General bisacsh Boundary value problems / Improperly posed problems fast Inverse problems (Differential equations) fast Mathematik Inverse problems (Differential equations) Boundary value problems Improperly posed problems Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | Mathematics MATHEMATICS / Differential Equations / General Boundary value problems / Improperly posed problems Inverse problems (Differential equations) Mathematik Boundary value problems Improperly posed problems Inkorrekt gestelltes Problem Inverses Problem |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=430031 |
| work_keys_str_mv | AT kabanikhinsi inverseandillposedproblemstheoryandapplications |