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Inverse Heat Conduction : Ill-Posed Problems / / Hamidreza Najafi [and three others]
| Inverse Heat Conduction : Ill-Posed Problems / / Hamidreza Najafi [and three others] |
| Autore | Najafi Hamidreza |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, Inc., , [2023] |
| Descrizione fisica | 1 online resource (355 pages) |
| Disciplina | 536.23 |
| Soggetto topico |
Heat - Conduction
Numerical analysis - Improperly posed problems |
| ISBN |
1-119-84022-8
1-119-84020-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title Page -- Copyright Page -- Contents -- List of Figures -- Nomenclature -- Preface to First Edition -- Preface to Second Edition -- Chapter 1 Inverse Heat Conduction Problems: An Overview -- 1.1 Introduction -- 1.2 Basic Mathematical Description -- 1.3 Classification of Methods -- 1.4 Function Estimation Versus Parameter Estimation -- 1.5 Other Inverse Function Estimation Problems -- 1.6 Early Works on IHCPs -- 1.7 Applications of IHCPs: A Modern Look -- 1.7.1 Manufacturing Processes -- 1.7.1.1 Machining Processes -- 1.7.1.2 Milling and Hot Forming -- 1.7.1.3 Quenching and Spray Cooling -- 1.7.1.4 Jet Impingement -- 1.7.1.5 Other Manufacturing Applications -- 1.7.2 Aerospace Applications -- 1.7.3 Biomedical Applications -- 1.7.4 Electronics Cooling -- 1.7.5 Instrumentation, Measurement, and Non-Destructive Testing -- 1.7.6 Other Applications -- 1.8 Measurements -- 1.8.1 Description of Measurement Errors -- 1.8.2 Statistical Description of Errors -- 1.9 Criteria for Evaluation of IHCP Methods -- 1.10 Scope of Book -- 1.11 Chapter Summary -- References -- Chapter 2 Analytical Solutions of Direct Heat Conduction Problems -- 2.1 Introduction -- 2.2 Numbering System -- 2.3 One-Dimensional Temperature Solutions -- 2.3.1 Generalized One-Dimensional Heat Transfer Problem -- 2.3.2 Cases of Interest -- 2.3.3 Dimensionless Variables -- 2.3.4 Exact Analytical Solution -- 2.3.5 The Concept of Computational Analytical Solution -- 2.3.5.1 Absolute and Relative Errors -- 2.3.5.2 Deviation Time -- 2.3.5.3 Second Deviation Time -- 2.3.5.4 Quasi-Steady, Steady-State and Unsteady Times -- 2.3.5.5 Solution for Large Times -- 2.3.5.6 Intrinsic Verification -- 2.3.6 X12B10T0 Case -- 2.3.6.1 Computational Analytical Solution -- 2.3.6.2 Computer Code and Plots -- 2.3.7 X12B20T0 Case -- 2.3.7.1 Computational Analytical Solution.
2.3.7.2 Computer Code and Plots -- 2.3.8 X22B10T0 Case -- 2.3.8.1 Computational Analytical Solution -- 2.3.8.2 Computer Code and Plots -- 2.3.9 X22B20T0 Case -- 2.3.9.1 Computational Analytical Solution -- 2.3.9.2 Computer Code and Plots -- 2.4 Two-Dimensional Temperature Solutions -- 2.4.1 Dimensionless Variables -- 2.4.2 Exact Analytical Solution -- 2.4.3 Computational Analytical Solution -- 2.4.3.1 Absolute and Relative Errors -- 2.4.3.2 One- and Two-Dimensional Deviation Times -- 2.4.3.3 Quasi-Steady Time -- 2.4.3.4 Number of Terms in the Quasi-Steady Solution with Eigenvalues in the Homogeneous Direction -- 2.4.3.5 Number of Terms in the Quasi-Steady Solution with Eigenvalues in the Nonhomogeneous Direction -- 2.4.3.6 Deviation Distance Alongx -- 2.4.3.7 Deviation Distance Alongy -- 2.4.3.8 Number of Terms in the Complementary Transient Solution -- 2.4.3.9 Computer Code and Plots -- 2.5 Chapter Summary -- Problems -- References -- Chapter 3 Approximate Methods for Direct Heat Conduction Problems -- 3.1 Introduction -- 3.1.1 Various Numerical Approaches -- 3.1.2 Scope of Chapter -- 3.2 Superposition Principles -- 3.2.1 Green's Function Solution Interpretation -- 3.2.2 Superposition Example - Step Pulse Heating -- 3.3 One-Dimensional Problem with Time-Dependent Surface Temperature -- 3.3.1 Piecewise-Constant Approximation -- 3.3.1.1 Superposition-Based Numerical Approximation of the Solution -- 3.3.1.2 Sequential-in-time Nature and Sensitivity Coefficients -- 3.3.1.3 Basic "Building Block" Solution -- 3.3.1.4 Computer Code and Example -- 3.3.1.5 Matrix Form of the Superposition-Based Numerical Approximation -- 3.3.2 Piecewise-Linear Approximation -- 3.3.2.1 Superposition-Based Numerical Approximation of the Solution -- 3.3.2.2 Sequential-in-time Nature and Sensitivity Coefficients -- 3.3.2.3 Basic "Building Block" Solutions. 3.3.2.4 Computer Code and Examples -- 3.3.2.5 Matrix Form of the Superposition-Based Numerical Approximation -- 3.4 One-Dimensional Problem with Time-Dependent Surface Heat Flux -- 3.4.1 Piecewise-Constant Approximation -- 3.4.1.1 Superposition-Based Numerical Approximation of the Solution -- 3.4.1.2 Heat Flux-Based Sensitivity Coefficients -- 3.4.1.3 Basic "Building Block" Solution -- 3.4.1.4 Computer Code and Example -- 3.4.1.5 Matrix Form of the Superposition-Based Numerical Approximation -- 3.4.2 Piecewise-Linear Approximation -- 3.4.2.1 Superposition-Based Numerical Approximation of the Solution -- 3.4.2.2 Heat Flux-Based Sensitivity Coefficients -- 3.4.2.3 Basic "Building Block" Solutions -- 3.4.2.4 Computer Code and Examples -- 3.4.2.5 Matrix Form of the Superposition-Based Numerical Approximation -- 3.5 Two-Dimensional Problem with Space-Dependent and Constant Surface Heat Flux -- 3.5.1 Piecewise-Uniform Approximation -- 3.5.1.1 Superposition-Based Numerical Approximation of the Solution -- 3.5.1.2 Heat Flux-Based Sensitivity Coefficients -- 3.5.1.3 Basic "Building Block" Solution -- 3.5.1.4 Computer Code and Examples -- 3.5.1.5 Matrix Form of the Superposition-Based Numerical Approximation -- 3.6 Two-Dimensional Problem with Space- and Time-Dependent Surface Heat Flux -- 3.6.1 Piecewise-Uniform Approximation -- 3.6.1.1 Numerical Approximation in Space -- 3.6.2 Piecewise-Constant Approximation -- 3.6.2.1 Numerical Approximation in Time -- 3.6.3 Superposition-Based Numerical Approximation of the Solution -- 3.6.3.1 Sequential-in-time Nature and Sensitivity Coefficients -- 3.6.3.2 Basic "Building Block" Solution -- 3.6.3.3 Computer Code and Example -- 3.6.3.4 Matrix Form of the Superposition-Based Numerical Approximation -- 3.7 Chapter Summary -- Problems -- References -- Chapter 4 Inverse Heat Conduction Estimation Procedures. 4.1 Introduction -- 4.2 Why is the IHCP Difficult? -- 4.2.1 Sensitivity to Errors -- 4.2.2 Damping and Lagging -- 4.2.2.1 Penetration Time -- 4.2.2.2 Importance of the Penetration Time -- 4.3 Ill-Posed Problems -- 4.3.1 An Exact Solution -- 4.3.2 Discrete System of Equations -- 4.3.3 The Need for Regularization -- 4.4 IHCP Solution Methodology -- 4.5 Sensitivity Coefficients -- 4.5.1 Definition of Sensitivity Coefficients and Linearity -- 4.5.2 One-Dimensional Sensitivity Coefficient Examples -- 4.5.2.1 X22 Plate Insulated on One Side -- 4.5.2.2 X12 Plate Insulated on One Side, Fixed Boundary Temperature -- 4.5.2.3 X32 Plate Insulated on One Side, Fixed Heat Transfer Coefficient -- 4.5.3 Two-Dimensional Sensitivity Coefficient Example -- 4.6 Stolz Method: Single Future Time Step Method -- 4.6.1 Introduction -- 4.6.2 Exact Matching of Measured Temperatures -- 4.7 Function Specification Method -- 4.7.1 Introduction -- 4.7.2 Sequential Function Specification Method -- 4.7.2.1 Piecewise Constant Functional Form -- 4.7.2.2 Piecewise Linear Functional Form -- 4.7.3 General Remarks About Function Specification Method -- 4.8 Tikhonov Regularization Method -- 4.8.1 Introduction -- 4.8.2 Physical Significance of Regularization Terms -- 4.8.2.1 Continuous Formulation -- 4.8.2.2 Discrete Formulation -- 4.8.3 Whole Domain TR Method -- 4.8.3.1 Matrix Formulation -- 4.8.4 Sequential TR Method -- 4.8.5 General Comments About Tikhonov Regularization -- 4.9 Gradient Methods -- 4.9.1 Conjugate Gradient Method -- 4.9.1.1 Fletcher-Reeves CGM -- 4.9.1.2 Polak-Ribiere CGM -- 4.9.2 Adjoint Method (Nonlinear Problems) -- 4.9.2.1 Some Necessary Mathematics -- 4.9.2.2 The Continuous Form of IHCP -- 4.9.2.3 The Sensitivity Problem -- 4.9.2.4 The Lagrangian and the Adjoint Problem -- 4.9.2.5 The Gradient Equation -- 4.9.2.6 Summary of IHCP solution by Adjoint Method. 4.9.2.7 Comments About Adjoint Method -- 4.9.3 General Comments about CGM -- 4.10 Truncated Singular Value Decomposition Method -- 4.10.1 SVD Concepts -- 4.10.2 TSVD in the IHCP -- 4.10.3 General Remarks About TSVD -- 4.11 Kalman Filter -- 4.11.1 Discrete Kalman Filter -- 4.11.2 Two Concepts for Applying Kalman Filter to IHCP -- 4.11.3 Scarpa and Milano Approach -- 4.11.3.1 Kalman Filter -- 4.11.3.2 Smoother -- 4.11.4 General Remarks About Kalman Filtering -- 4.12 Chapter Summary -- Problems -- References -- Chapter 5 Filter Form of IHCP Solution -- 5.1 Introduction -- 5.2 Temperature Perturbation Approach -- 5.3 Filter Matrix Perspective -- 5.3.1 Function Specification Method -- 5.3.2 Tikhonov Regularization -- 5.3.3 Singular Value Decomposition -- 5.3.4 Conjugate Gradient -- 5.4 Sequential Filter Form -- 5.5 Using Second Temperature Sensor as Boundary Condition -- 5.5.1 Exact Solution for the Direct Problem -- 5.5.2 Tikhonov Regularization Method as IHCP Solution -- 5.5.3 Filter Form of IHCP Solution -- 5.6 Filter Coefficients for Multi-Layer Domain -- 5.6.1 Solution Strategy for IHCP in Multi-Layer Domain -- 5.6.1.1 Inner Layer -- 5.6.1.2 Outer Layer -- 5.6.1.3 Combined Solution -- 5.6.2 Filter Form of the Solution -- 5.7 Filter Coefficients for Non-Linear IHCP: Application for Heat Flux Measurement Using Directional Flame Thermometer -- 5.7.1 Solution for the IHCP -- 5.7.1.1 Back Layer (Insulation) -- 5.7.1.2 Front Layer (Inconel plate) -- 5.7.1.3 Combined Solution -- 5.7.2 Filter form of the solution -- 5.7.3 Accounting for Temperature-Dependent Material Properties -- 5.7.4 Examples -- 5.8 Chapter Summary -- Problems -- References -- Chapter 6 Optimal Regularization -- 6.1 Preliminaries -- 6.1.1 Some Mathematics -- 6.1.2 Design vs. Experimental Setting -- 6.2 Two Conflicting Objectives -- 6.2.1 Minimum Deterministic Bias. 6.2.2 Minimum Sensitivity to Random Errors. |
| Record Nr. | UNINA-9910830226803321 |
Najafi Hamidreza
|
||
| Hoboken, New Jersey : , : John Wiley & Sons, Inc., , [2023] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Journal of inverse and ill-posed problems
| Journal of inverse and ill-posed problems |
| Pubbl/distr/stampa | Zeist, the Netherlands, : VSP BV, 1993- |
| Descrizione fisica | 1 online resource |
| Disciplina | 515.3 |
| Soggetto topico |
Inverse problems (Differential equations)
Numerical analysis - Improperly posed problems Differential Equations |
| Soggetto genere / forma | Periodicals. |
| ISSN | 1569-3945 |
| Formato | Materiale a stampa |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Altri titoli varianti | Inverse and ill-posed problems |
| Record Nr. | UNISA-996231338303316 |
| Zeist, the Netherlands, : VSP BV, 1993- | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Journal of inverse and ill-posed problems
| Journal of inverse and ill-posed problems |
| Pubbl/distr/stampa | Zeist, the Netherlands, : VSP BV, 1993- |
| Descrizione fisica | 1 online resource |
| Disciplina | 515.3 |
| Soggetto topico |
Inverse problems (Differential equations)
Numerical analysis - Improperly posed problems Differential Equations |
| Soggetto genere / forma | Periodicals. |
| ISSN | 1569-3945 |
| Formato | Materiale a stampa |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Altri titoli varianti | Inverse and ill-posed problems |
| Record Nr. | UNINA-9910449248103321 |
| Zeist, the Netherlands, : VSP BV, 1993- | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Journal of inverse and ill-posed problems
| Journal of inverse and ill-posed problems |
| Pubbl/distr/stampa | Zeist, the Netherlands, : VSP BV, 1993- |
| Descrizione fisica | 1 online resource |
| Disciplina | 515.3 |
| Soggetto topico |
Inverse problems (Differential equations)
Numerical analysis - Improperly posed problems Differential Equations Problèmes inverses (Équations différentielles) Analyse numérique - Problèmes mal posés |
| Soggetto genere / forma | Periodicals. |
| ISSN | 1569-3945 |
| Formato | Materiale a stampa |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Altri titoli varianti | Inverse and ill-posed problems |
| Record Nr. | UNINA-9910799268803321 |
| Zeist, the Netherlands, : VSP BV, 1993- | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The mollification method and the numerical solution of ill-posed problems [[electronic resource] /] / Diego A. Murio
| The mollification method and the numerical solution of ill-posed problems [[electronic resource] /] / Diego A. Murio |
| Autore | Murio Diego A. <1944-> |
| Pubbl/distr/stampa | New York, : Wiley, c1993 |
| Descrizione fisica | 1 online resource (272 p.) |
| Disciplina |
515.353
515/.353 |
| Soggetto topico |
Numerical analysis - Improperly posed problems
Inverse problems (Differential equations) - Numerical solutions |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-10099-1
9786613100993 1-118-03146-6 1-118-03321-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
The Mollification Method and the Numerical Solution of Ill-Posed Problems; Contents; Preface; Acknowledgments; 1. Numerical Differentiation; 1.1. Description of the Problem; 1.2. Stabilized Problem; 1.3. Differentiation as an Inverse Problem; 1.4. Parameter Selection; 1.5. Numerical Procedure; 1.6. Numerical Results; 1.7. Exercises; 1.8. References and Comments; 2. Abel's Integral Equation; 2.1. Description of the Problem; 2.2. Stabilized Problems; 2.3. Numerical Implementations; 2.4. Numerical Results and Comparisons; 2.5. Exercises; 2.6. References and Comments
3. Inverse Heat Conduction Problem3.1. One-Dimensional IHCP in a Semi-infinite Body; 3.2. Stabilized Problems; 3.3. One-Dimensional IHCP with Finite Slab Symmetry; 3.4. Finite-Difference Approximations; 3.5. Integral Equation Approximations; 3.6. Numerical Results; 3.7. Exercises; 3.8. References and Comments; 4. Two-Dimensional Inverse Heat Conduction Problem; 4.1. Two-Dimensional IHCP in a Semi-infinite Slab; 4.2. Stabilized Problem; 4.3. Numerical Procedure and Error Analysis; 4.4. Numerical Results; 4.5. Exercises; 4.6. References and Comments 5. Applications of the Space Marching Solution of the IHCP5.1. Identification of Boundary Source Functions; 5.2. Numerical Procedure; 5.3. IHCP with Phase Changes; 5.4. Description of the Problems; 5.5. Numerical Procedure; 5.6. Identification of the Initial Temperature Distribution; 5.7. Semi-infinite Body; 5.8. Finite Slab Symmetry; 5.9. Stabilized Problems; 5.10. Numerical Results; 5.11. Exercises; 5.12. References and Comments; 6. Applications of Stable Numerical Differentiation Procedures; 6.1. Numerical Identification of Forcing Terms; 6.2. Stabilized Problem; 6.3. Numerical Results 6.4. Identification of the Transmissivity Coefficient in the One-Dimensional Elliptic Equation6.5. Stability Analysis; 6.6. Numerical Method; 6.7. Numerical Results; 6.8. Identification of the Transmissivity Coefficient in the One-Dimensional Parabolic Equation; 6.9. Stability Analysis; 6.10. Numerical Method; 6.11. Numerical Results; 6.12. Exercises; 6.13. References and Comments; Appendix A. Mathematical Background; A.1. Lp Spaces; A.2. The Hilbert Space L2(Ω); A.3. Approximation of Functions in L2(Ω); A.4. Mollifiers; A.5. Fourier Transform; A.6. Discrete Functions A.7. References and CommentsAppendix B. References to the Literature on the IHCP; Index |
| Record Nr. | UNINA-9910133453103321 |
|
Murio Diego A. <1944->
|
||
| New York, : Wiley, c1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The mollification method and the numerical solution of ill-posed problems [[electronic resource] /] / Diego A. Murio
| The mollification method and the numerical solution of ill-posed problems [[electronic resource] /] / Diego A. Murio |
| Autore | Murio Diego A. <1944-> |
| Pubbl/distr/stampa | New York, : Wiley, c1993 |
| Descrizione fisica | 1 online resource (272 p.) |
| Disciplina |
515.353
515/.353 |
| Soggetto topico |
Numerical analysis - Improperly posed problems
Inverse problems (Differential equations) - Numerical solutions |
| ISBN |
1-283-10099-1
9786613100993 1-118-03146-6 1-118-03321-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
The Mollification Method and the Numerical Solution of Ill-Posed Problems; Contents; Preface; Acknowledgments; 1. Numerical Differentiation; 1.1. Description of the Problem; 1.2. Stabilized Problem; 1.3. Differentiation as an Inverse Problem; 1.4. Parameter Selection; 1.5. Numerical Procedure; 1.6. Numerical Results; 1.7. Exercises; 1.8. References and Comments; 2. Abel's Integral Equation; 2.1. Description of the Problem; 2.2. Stabilized Problems; 2.3. Numerical Implementations; 2.4. Numerical Results and Comparisons; 2.5. Exercises; 2.6. References and Comments
3. Inverse Heat Conduction Problem3.1. One-Dimensional IHCP in a Semi-infinite Body; 3.2. Stabilized Problems; 3.3. One-Dimensional IHCP with Finite Slab Symmetry; 3.4. Finite-Difference Approximations; 3.5. Integral Equation Approximations; 3.6. Numerical Results; 3.7. Exercises; 3.8. References and Comments; 4. Two-Dimensional Inverse Heat Conduction Problem; 4.1. Two-Dimensional IHCP in a Semi-infinite Slab; 4.2. Stabilized Problem; 4.3. Numerical Procedure and Error Analysis; 4.4. Numerical Results; 4.5. Exercises; 4.6. References and Comments 5. Applications of the Space Marching Solution of the IHCP5.1. Identification of Boundary Source Functions; 5.2. Numerical Procedure; 5.3. IHCP with Phase Changes; 5.4. Description of the Problems; 5.5. Numerical Procedure; 5.6. Identification of the Initial Temperature Distribution; 5.7. Semi-infinite Body; 5.8. Finite Slab Symmetry; 5.9. Stabilized Problems; 5.10. Numerical Results; 5.11. Exercises; 5.12. References and Comments; 6. Applications of Stable Numerical Differentiation Procedures; 6.1. Numerical Identification of Forcing Terms; 6.2. Stabilized Problem; 6.3. Numerical Results 6.4. Identification of the Transmissivity Coefficient in the One-Dimensional Elliptic Equation6.5. Stability Analysis; 6.6. Numerical Method; 6.7. Numerical Results; 6.8. Identification of the Transmissivity Coefficient in the One-Dimensional Parabolic Equation; 6.9. Stability Analysis; 6.10. Numerical Method; 6.11. Numerical Results; 6.12. Exercises; 6.13. References and Comments; Appendix A. Mathematical Background; A.1. Lp Spaces; A.2. The Hilbert Space L2(Ω); A.3. Approximation of Functions in L2(Ω); A.4. Mollifiers; A.5. Fourier Transform; A.6. Discrete Functions A.7. References and CommentsAppendix B. References to the Literature on the IHCP; Index |
| Record Nr. | UNINA-9910830662103321 |
|
Murio Diego A. <1944->
|
||
| New York, : Wiley, c1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The mollification method and the numerical solution of ill-posed problems / / Diego A. Murio
| The mollification method and the numerical solution of ill-posed problems / / Diego A. Murio |
| Autore | Murio Diego A. <1944-> |
| Pubbl/distr/stampa | New York, : Wiley, c1993 |
| Descrizione fisica | 1 online resource (272 p.) |
| Disciplina |
515.353
515/.353 |
| Soggetto topico |
Numerical analysis - Improperly posed problems
Inverse problems (Differential equations) - Numerical solutions |
| ISBN |
1-283-10099-1
9786613100993 1-118-03146-6 1-118-03321-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
The Mollification Method and the Numerical Solution of Ill-Posed Problems; Contents; Preface; Acknowledgments; 1. Numerical Differentiation; 1.1. Description of the Problem; 1.2. Stabilized Problem; 1.3. Differentiation as an Inverse Problem; 1.4. Parameter Selection; 1.5. Numerical Procedure; 1.6. Numerical Results; 1.7. Exercises; 1.8. References and Comments; 2. Abel's Integral Equation; 2.1. Description of the Problem; 2.2. Stabilized Problems; 2.3. Numerical Implementations; 2.4. Numerical Results and Comparisons; 2.5. Exercises; 2.6. References and Comments
3. Inverse Heat Conduction Problem3.1. One-Dimensional IHCP in a Semi-infinite Body; 3.2. Stabilized Problems; 3.3. One-Dimensional IHCP with Finite Slab Symmetry; 3.4. Finite-Difference Approximations; 3.5. Integral Equation Approximations; 3.6. Numerical Results; 3.7. Exercises; 3.8. References and Comments; 4. Two-Dimensional Inverse Heat Conduction Problem; 4.1. Two-Dimensional IHCP in a Semi-infinite Slab; 4.2. Stabilized Problem; 4.3. Numerical Procedure and Error Analysis; 4.4. Numerical Results; 4.5. Exercises; 4.6. References and Comments 5. Applications of the Space Marching Solution of the IHCP5.1. Identification of Boundary Source Functions; 5.2. Numerical Procedure; 5.3. IHCP with Phase Changes; 5.4. Description of the Problems; 5.5. Numerical Procedure; 5.6. Identification of the Initial Temperature Distribution; 5.7. Semi-infinite Body; 5.8. Finite Slab Symmetry; 5.9. Stabilized Problems; 5.10. Numerical Results; 5.11. Exercises; 5.12. References and Comments; 6. Applications of Stable Numerical Differentiation Procedures; 6.1. Numerical Identification of Forcing Terms; 6.2. Stabilized Problem; 6.3. Numerical Results 6.4. Identification of the Transmissivity Coefficient in the One-Dimensional Elliptic Equation6.5. Stability Analysis; 6.6. Numerical Method; 6.7. Numerical Results; 6.8. Identification of the Transmissivity Coefficient in the One-Dimensional Parabolic Equation; 6.9. Stability Analysis; 6.10. Numerical Method; 6.11. Numerical Results; 6.12. Exercises; 6.13. References and Comments; Appendix A. Mathematical Background; A.1. Lp Spaces; A.2. The Hilbert Space L2(Ω); A.3. Approximation of Functions in L2(Ω); A.4. Mollifiers; A.5. Fourier Transform; A.6. Discrete Functions A.7. References and CommentsAppendix B. References to the Literature on the IHCP; Index |
| Record Nr. | UNINA-9910877366903321 |
|
Murio Diego A. <1944->
|
||
| New York, : Wiley, c1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Regularization theory for ill-posed problems : selected topics / / by Shuai Lu, Sergei V. Pereverzev
| Regularization theory for ill-posed problems : selected topics / / by Shuai Lu, Sergei V. Pereverzev |
| Autore | Lu Shuai <1976-> |
| Pubbl/distr/stampa | Berlin ; ; Boston : , : Walter de Gruyter, , [2013] |
| Descrizione fisica | 1 online resource (304 p.) |
| Disciplina | 518/.53 |
| Altri autori (Persone) | PereverzevSergei V |
| Collana | Inverse and ill-posed problems series |
| Soggetto topico |
Numerical analysis - Improperly posed problems
Numerical differentiation |
| Soggetto genere / forma | Electronic books. |
| ISBN | 3-11-028649-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Preface -- Contents -- Chapter 1. An introduction using classical examples -- Chapter 2. Basics of single parameter regularization schemes -- Chapter 3. Multiparameter regularization -- Chapter 4. Regularization algorithms in learning theory -- Chapter 5. Meta-learning approach to regularization - case study: blood glucose prediction -- Bibliography -- Index |
| Record Nr. | UNINA-9910462704103321 |
|
Lu Shuai <1976->
|
||
| Berlin ; ; Boston : , : Walter de Gruyter, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Regularization theory for ill-posed problems : selected topics / / by Shuai Lu, Sergei V. Pereverzev
| Regularization theory for ill-posed problems : selected topics / / by Shuai Lu, Sergei V. Pereverzev |
| Autore | Lu Shuai <1976-> |
| Pubbl/distr/stampa | Berlin ; ; Boston : , : Walter de Gruyter, , [2013] |
| Descrizione fisica | 1 online resource (304 p.) |
| Disciplina | 518/.53 |
| Altri autori (Persone) | PereverzevSergei V |
| Collana | Inverse and ill-posed problems series |
| Soggetto topico |
Numerical analysis - Improperly posed problems
Numerical differentiation |
| Soggetto non controllato |
Balancing Principle
Blood Glucose Prediction Convergence Rate Discrepancy Principle Error Bound Estimation Ill-posed Problem Learning Theory, Meta-learning Multi-parameter Regularization Regularization Method |
| ISBN | 3-11-028649-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Preface -- Contents -- Chapter 1. An introduction using classical examples -- Chapter 2. Basics of single parameter regularization schemes -- Chapter 3. Multiparameter regularization -- Chapter 4. Regularization algorithms in learning theory -- Chapter 5. Meta-learning approach to regularization - case study: blood glucose prediction -- Bibliography -- Index |
| Record Nr. | UNINA-9910787646303321 |
|
Lu Shuai <1976->
|
||
| Berlin ; ; Boston : , : Walter de Gruyter, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Regularization theory for ill-posed problems : selected topics / / by Shuai Lu, Sergei V. Pereverzev
| Regularization theory for ill-posed problems : selected topics / / by Shuai Lu, Sergei V. Pereverzev |
| Autore | Lu Shuai <1976-> |
| Pubbl/distr/stampa | Berlin ; ; Boston : , : Walter de Gruyter, , [2013] |
| Descrizione fisica | 1 online resource (304 p.) |
| Disciplina | 518/.53 |
| Altri autori (Persone) | PereverzevSergei V |
| Collana | Inverse and ill-posed problems series |
| Soggetto topico |
Numerical analysis - Improperly posed problems
Numerical differentiation |
| Soggetto non controllato |
Balancing Principle
Blood Glucose Prediction Convergence Rate Discrepancy Principle Error Bound Estimation Ill-posed Problem Learning Theory, Meta-learning Multi-parameter Regularization Regularization Method |
| ISBN | 3-11-028649-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Preface -- Contents -- Chapter 1. An introduction using classical examples -- Chapter 2. Basics of single parameter regularization schemes -- Chapter 3. Multiparameter regularization -- Chapter 4. Regularization algorithms in learning theory -- Chapter 5. Meta-learning approach to regularization - case study: blood glucose prediction -- Bibliography -- Index |
| Record Nr. | UNINA-9910823913803321 |
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Lu Shuai <1976->
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| Berlin ; ; Boston : , : Walter de Gruyter, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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