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Computer modelling in tomography and ill-posed problems / / M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov
| Computer modelling in tomography and ill-posed problems / / M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov |
| Autore | Lavrentʹev M. M (Mikhail Mikhaĭlovich) |
| Edizione | [Reprint 2014] |
| Pubbl/distr/stampa | Utrecht ; ; Boston : , : VSP, , 2001 |
| Descrizione fisica | 1 online resource (136 pages) : illustrations |
| Disciplina | 516 |
| Collana | Inverse and ill-posed problems series |
| Soggetto topico |
Geometric tomography
Inverse problems (Differential equations) |
| Soggetto non controllato |
Algorithms
Calculation Mathematics Cone-beam Ill-posed Problems Inverse Kinematic Problem Regularization Tomography |
| ISBN | 3-11-094093-0 |
| Classificazione | ST 640 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Machine generated contents note: Chapter 1. Mathematical basis of the method of computerized -- tomography 11 -- 1.1. Basic notions of the theory of ill-posed problems11 -- 1.2. Problem of integral geometry16 -- 1.3. The Radon transform18 -- 1.4. Radon problem as an example of an ill-posed problem20 -- 1.5. The algorithm of inversion of the two-dimensional Radon -- transform based on the convolution with the generalized -- function l/z225 -- Chapter 2. Cone-beam tomography reconstruction 33 -- 2.1. Reducing the inversion formulas of cone-beam tomography recont -- struction to the form convenient for constructing numerical -- algorithm s33 -- 2.2. Elements of the theory of generalized functions in application to -- problems of inversion of the ray transformation45 -- 2.3. The relations between the Radon, Fourier, -- and ray transformations51 -- Chapter 3. Inverse kinematic problem -- in the tomographic setting 55 -- 3.1. Direct kinematic problem and numerical solution -- for three-dimensional regular media55 -- 3.2. Formulation of the inverse kinematic problem with the use of -- a tomography system of data gathering66 -- 3.3. Deduction of the basic inversion formula and the algorithm of -- solving the inverse kinematic problem in -- three-dimensional linearized formulation68 -- 3.4. Model experiment and numerical study of the algorithm79 -- 3.5. Solution of the inverse kinematic problem by the method of -- computerized tomography for media with opaque inclusions 98 -- Appendix: Reconstruction with the use -- of the standard model 112 -- Bibliography 119. |
| Record Nr. | UNINA-9910788955503321 |
Lavrentʹev M. M (Mikhail Mikhaĭlovich)
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| Utrecht ; ; Boston : , : VSP, , 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computer modelling in tomography and ill-posed problems / / M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov
| Computer modelling in tomography and ill-posed problems / / M.M. Lavrentèv, S.M. Zerkal and O.E. Trofimov |
| Autore | Lavrentʹev M. M (Mikhail Mikhaĭlovich) |
| Edizione | [Reprint 2014] |
| Pubbl/distr/stampa | Utrecht ; ; Boston : , : VSP, , 2001 |
| Descrizione fisica | 1 online resource (136 pages) : illustrations |
| Disciplina | 516 |
| Collana | Inverse and ill-posed problems series |
| Soggetto topico |
Geometric tomography
Inverse problems (Differential equations) |
| Soggetto non controllato |
Algorithms
Calculation Mathematics Cone-beam Ill-posed Problems Inverse Kinematic Problem Regularization Tomography |
| ISBN | 3-11-094093-0 |
| Classificazione | ST 640 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Machine generated contents note: Chapter 1. Mathematical basis of the method of computerized -- tomography 11 -- 1.1. Basic notions of the theory of ill-posed problems11 -- 1.2. Problem of integral geometry16 -- 1.3. The Radon transform18 -- 1.4. Radon problem as an example of an ill-posed problem20 -- 1.5. The algorithm of inversion of the two-dimensional Radon -- transform based on the convolution with the generalized -- function l/z225 -- Chapter 2. Cone-beam tomography reconstruction 33 -- 2.1. Reducing the inversion formulas of cone-beam tomography recont -- struction to the form convenient for constructing numerical -- algorithm s33 -- 2.2. Elements of the theory of generalized functions in application to -- problems of inversion of the ray transformation45 -- 2.3. The relations between the Radon, Fourier, -- and ray transformations51 -- Chapter 3. Inverse kinematic problem -- in the tomographic setting 55 -- 3.1. Direct kinematic problem and numerical solution -- for three-dimensional regular media55 -- 3.2. Formulation of the inverse kinematic problem with the use of -- a tomography system of data gathering66 -- 3.3. Deduction of the basic inversion formula and the algorithm of -- solving the inverse kinematic problem in -- three-dimensional linearized formulation68 -- 3.4. Model experiment and numerical study of the algorithm79 -- 3.5. Solution of the inverse kinematic problem by the method of -- computerized tomography for media with opaque inclusions 98 -- Appendix: Reconstruction with the use -- of the standard model 112 -- Bibliography 119. |
| Record Nr. | UNINA-9910813739403321 |
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Lavrentʹev M. M (Mikhail Mikhaĭlovich)
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| Utrecht ; ; Boston : , : VSP, , 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Ill-posed boundary-value problems / / S.E. Temirbolat
| Ill-posed boundary-value problems / / S.E. Temirbolat |
| Autore | Temirbolat S. E |
| Edizione | [Reprint 2012] |
| Pubbl/distr/stampa | Utrecht ; ; Boston : , : VSP, , 2003 |
| Descrizione fisica | 1 online resource (152 pages) : illustrations |
| Disciplina | 515/.35 |
| Collana |
Inverse and Ill-Posed Problems Series
Inverse and ill-posed problems series |
| Soggetto topico | Boundary value problems |
| Soggetto non controllato |
Boundary-Value Problems
Constant Coefficients Differential Equations First-Order Ill-posed Problems |
| ISBN | 3-11-091551-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Preface -- Contents -- Introduction -- Chapter 1. Construction of ill-posed problems for a system of the first order ODE -- Chapter 2. Parabolic problems -- Chapter 3. Hyperbolic equations -- Bibliography |
| Record Nr. | UNINA-9910789097503321 |
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Temirbolat S. E
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| Utrecht ; ; Boston : , : VSP, , 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Ill-posed boundary-value problems / / S.E. Temirbolat
| Ill-posed boundary-value problems / / S.E. Temirbolat |
| Autore | Temirbolat S. E |
| Edizione | [Reprint 2012] |
| Pubbl/distr/stampa | Utrecht ; ; Boston : , : VSP, , 2003 |
| Descrizione fisica | 1 online resource (152 pages) : illustrations |
| Disciplina | 515/.35 |
| Collana |
Inverse and Ill-Posed Problems Series
Inverse and ill-posed problems series |
| Soggetto topico | Boundary value problems |
| Soggetto non controllato |
Boundary-Value Problems
Constant Coefficients Differential Equations First-Order Ill-posed Problems |
| ISBN | 3-11-091551-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Preface -- Contents -- Introduction -- Chapter 1. Construction of ill-posed problems for a system of the first order ODE -- Chapter 2. Parabolic problems -- Chapter 3. Hyperbolic equations -- Bibliography |
| Record Nr. | UNINA-9910816768403321 |
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Temirbolat S. E
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| Utrecht ; ; Boston : , : VSP, , 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Inverse and ill-posed problems [[electronic resource] ] : theory and applications / / Sergey I. Kabanikhin
| Inverse and ill-posed problems [[electronic resource] ] : theory and applications / / Sergey I. Kabanikhin |
| Autore | Kabanikhin S. I |
| Pubbl/distr/stampa | Berlin ; ; Boston, : De Gruyter, c2012 |
| Descrizione fisica | 1 online resource (475 p.) |
| Disciplina | 515/.357 |
| Collana | Inverse and ill-posed problems series |
| Soggetto topico |
Inverse problems (Differential equations)
Boundary value problems - Improperly posed problems |
| Soggetto non controllato |
Differential Equation
Ill-posed Problems Integral Equation Inverse Problem Regularization |
| ISBN | 3-11-022401-1 |
| Classificazione | SK 950 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Preface / Kabanikhin, Sergey I. -- Denotations -- Contents -- Chapter 1. Basic concepts and examples -- Chapter 2. Ill-posed problems -- Chapter 3. Ill-posed problems of linear algebra -- Chapter 4. Integral equations -- Chapter 5. Integral geometry -- Chapter 6. Inverse spectral and scattering problems -- Chapter 7. Linear problems for hyperbolic equations -- Chapter 8. Linear problems for parabolic equations -- Chapter 9. Linear problems for elliptic equations -- Chapter 10. Inverse coefficient problems for hyperbolic equations -- Chapter 11. Inverse coefficient problems for parabolic and elliptic equations -- Appendix A -- Appendix B -- Epilogue -- Bibliography -- Index |
| Record Nr. | UNINA-9910791969603321 |
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Kabanikhin S. I
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| Berlin ; ; Boston, : De Gruyter, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Inverse and ill-posed problems : theory and applications / / Sergey I. Kabanikhin
| Inverse and ill-posed problems : theory and applications / / Sergey I. Kabanikhin |
| Autore | Kabanikhin S. I |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Berlin ; ; Boston, : De Gruyter, c2012 |
| Descrizione fisica | 1 online resource (475 p.) |
| Disciplina |
515/.357
515.3570000000 |
| Collana | Inverse and ill-posed problems series |
| Soggetto topico |
Inverse problems (Differential equations)
Boundary value problems - Improperly posed problems |
| Soggetto non controllato |
Differential Equation
Ill-posed Problems Integral Equation Inverse Problem Regularization |
| ISBN | 3-11-022401-1 |
| Classificazione | SK 950 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Preface / Kabanikhin, Sergey I. -- Denotations -- Contents -- Chapter 1. Basic concepts and examples -- Chapter 2. Ill-posed problems -- Chapter 3. Ill-posed problems of linear algebra -- Chapter 4. Integral equations -- Chapter 5. Integral geometry -- Chapter 6. Inverse spectral and scattering problems -- Chapter 7. Linear problems for hyperbolic equations -- Chapter 8. Linear problems for parabolic equations -- Chapter 9. Linear problems for elliptic equations -- Chapter 10. Inverse coefficient problems for hyperbolic equations -- Chapter 11. Inverse coefficient problems for parabolic and elliptic equations -- Appendix A -- Appendix B -- Epilogue -- Bibliography -- Index |
| Record Nr. | UNINA-9910826518503321 |
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Kabanikhin S. I
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| Berlin ; ; Boston, : De Gruyter, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Operators and iterative processes of fejér type [[electronic resource] ] : theory and applications / / Vladimir V. Vasin, Ivan I. Eremin
| Operators and iterative processes of fejér type [[electronic resource] ] : theory and applications / / Vladimir V. Vasin, Ivan I. Eremin |
| Autore | Vasin Vladimir V |
| Pubbl/distr/stampa | Berlin ; ; New York, : W. de Gruyter, c2009 |
| Descrizione fisica | 1 online resource (169 p.) |
| Disciplina | 515.7 |
| Altri autori (Persone) | EreminI. I (Ivan Ivanovich) |
| Collana | Inverse and iII-posed problems series |
| Soggetto topico |
Iterative methods (Mathematics)
Numerical analysis |
| Soggetto non controllato |
Ill-posed Problems
Iteration Method Noisy Data Nonlinear Equations Optimization |
| ISBN |
1-282-18795-3
9786612187957 3-11-021819-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Introduction -- Chapter I. General properties of nonlinear operators of Fejér type -- Chapter II. Applications of iterative processes to nonlinear equations -- Chapter III. Application of Fejér methods to solve linear and convex inequalities -- Chapter IV. Some topics of Fejér mappings and processes -- Backmatter |
| Record Nr. | UNINA-9910778496003321 |
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Vasin Vladimir V
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| Berlin ; ; New York, : W. de Gruyter, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Operators and iterative processes of fejér type : theory and applications / / Vladimir V. Vasin, Ivan I. Eremin
| Operators and iterative processes of fejér type : theory and applications / / Vladimir V. Vasin, Ivan I. Eremin |
| Autore | Vasin Vladimir V |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Berlin ; ; New York, : W. de Gruyter, c2009 |
| Descrizione fisica | 1 online resource (169 p.) |
| Disciplina | 515.7 |
| Altri autori (Persone) | EreminI. I (Ivan Ivanovich) |
| Collana | Inverse and iII-posed problems series |
| Soggetto topico |
Iterative methods (Mathematics)
Numerical analysis |
| Soggetto non controllato |
Ill-posed Problems
Iteration Method Noisy Data Nonlinear Equations Optimization |
| ISBN |
1-282-18795-3
9786612187957 3-11-021819-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Introduction -- Chapter I. General properties of nonlinear operators of Fejér type -- Chapter II. Applications of iterative processes to nonlinear equations -- Chapter III. Application of Fejér methods to solve linear and convex inequalities -- Chapter IV. Some topics of Fejér mappings and processes -- Backmatter |
| Record Nr. | UNINA-9910828377803321 |
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Vasin Vladimir V
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| Berlin ; ; New York, : W. de Gruyter, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Well-posed, ill-posed, and intermediate problems with applications [[electronic resource] /] / Yu. P. Petrov and V.S. Sizikov
| Well-posed, ill-posed, and intermediate problems with applications [[electronic resource] /] / Yu. P. Petrov and V.S. Sizikov |
| Autore | Petrov Yu. P |
| Pubbl/distr/stampa | Leiden ; ; Boston, : VSP, c2005 |
| Descrizione fisica | 1 online resource (244 p.) |
| Disciplina |
515.35
518/.6 |
| Altri autori (Persone) | SizikovV. S (Valeriĭ Sergeevich) |
| Collana | Inverse and ill-posed problems series |
| Soggetto topico |
Differential equations - Numerical solutions
Numerical analysis - Improperly posed problems Engineering mathematics Mathematical physics |
| Soggetto non controllato |
Ill-posed Problems
Intermediate Problems Well-posed Problems |
| ISBN |
1-280-86872-4
9786610868728 1-4294-2711-6 90-474-1194-3 3-11-019530-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Preface -- Contents -- Part I. Three classes of problems in mathematics, physics, and engineering -- Chapter 1. Simplest ill-posed problems -- Chapter 2. Problems intermediate between well- and ill-posed problems -- Chapter 3. Change of sensitivity to measurement errors under integral transformations used in modeling of ships and marine control systems -- Bibliography to Part I -- Part II. Stable methods for solving inverse problems -- Chapter 4. Regular methods for solving ill-posed problems -- Chapter 5. Inverse problems in image reconstruction and tomography -- Bibliography to Part II -- Index |
| Record Nr. | UNINA-9910784029403321 |
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Petrov Yu. P
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| Leiden ; ; Boston, : VSP, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Well-posed, ill-posed, and intermediate problems with applications / / Yu. P. Petrov and V.S. Sizikov
| Well-posed, ill-posed, and intermediate problems with applications / / Yu. P. Petrov and V.S. Sizikov |
| Autore | Petrov Yu. P |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Leiden ; ; Boston, : VSP, c2005 |
| Descrizione fisica | 1 online resource (244 p.) |
| Disciplina |
515.35
518/.6 |
| Altri autori (Persone) | SizikovV. S (Valeriĭ Sergeevich) |
| Collana | Inverse and ill-posed problems series |
| Soggetto topico |
Differential equations - Numerical solutions
Numerical analysis - Improperly posed problems Engineering mathematics Mathematical physics |
| Soggetto non controllato |
Ill-posed Problems
Intermediate Problems Well-posed Problems |
| ISBN |
1-280-86872-4
9786610868728 1-4294-2711-6 90-474-1194-3 3-11-019530-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Preface -- Contents -- Part I. Three classes of problems in mathematics, physics, and engineering -- Chapter 1. Simplest ill-posed problems -- Chapter 2. Problems intermediate between well- and ill-posed problems -- Chapter 3. Change of sensitivity to measurement errors under integral transformations used in modeling of ships and marine control systems -- Bibliography to Part I -- Part II. Stable methods for solving inverse problems -- Chapter 4. Regular methods for solving ill-posed problems -- Chapter 5. Inverse problems in image reconstruction and tomography -- Bibliography to Part II -- Index |
| Record Nr. | UNINA-9910807973003321 |
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Petrov Yu. P
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| Leiden ; ; Boston, : VSP, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||