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Guaranteed estimation problems in the theory of linear ordinary differential equations with uncertain data / / Oleksandr Nakonechnyi and Yuri Podlipenko
| Guaranteed estimation problems in the theory of linear ordinary differential equations with uncertain data / / Oleksandr Nakonechnyi and Yuri Podlipenko |
| Autore | Nakonechnyi O. |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Gistrup, Denmark ; ; London ; ; New York, New York : , : River Publishers : , : Routledge, , [2021] |
| Descrizione fisica | 1 online resource (234 pages) |
| Disciplina | 515.353 |
| Collana | River Publishers series in mathematical and engineering sciences |
| Soggetto topico |
Cauchy problem
Differential equations, Linear Estimation theory |
| ISBN |
1-00-333836-4
1-003-33836-4 1-000-79513-6 87-7022-631-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover -- Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data -- Contents -- Preface -- Introduction -- 1 Guaranteed Estimates of Solutions and Right-Hand Sides of the Cauchy Problem Under Incomplete Data -- 1.1 Preliminaries and Auxiliary Results -- 1.2 Statement of the Estimation Problem -- 1.3 Minimax Estimation of Functionals From Solutions of the Cauchy Problem -- 1.4 1-Optimal Estimates of Unknown Solution of the Cauchy Problem -- 1.5 Representations of Guaranteed Estimates of Functionals -- 1.6 Minimax Estimation of the Right-Hand Sides of Equalities that Enter -- 1.7 Guaranteed Estimation of Solutions to the Cauchy Problem -- 1.8 Guaranteed Predictive Estimation of Solutions to the Cauchy Problem -- 2 Guaranteed Estimation of Unknown Solutions and Right-Hand Sides of First Order Linear Systems of Periodic ODEs -- 2.1 Guaranteed Estimation of Solutions of First Order Linear Systems -- 2.2 Guaranteed Recovery of Unknown Right-Hand Sides -- 2.3 Guaranteed a Posteriori Estimation of Unknown Right-Hand Sides -- 3 Guaranteed Estimation of Solutions of Boundary Value Problems for Linear Ordinary Differential Equations with Decomposed Boundary Data -- 3.1 Preliminaries and Auxiliary Results -- 3.2 Statement of the Minimax Estimation Problem and Its Reduction -- 3.3 Representations for Minimax Estimates of Functionals from Solutions -- 3.4 Minimax Estimates of Solutions Subject to Incomplete Restrictions -- 3.5 Elimination Technique in Minimax Estimation Problems -- 3.6 Minimax Estimation of the Solutions to the Boundary Value Problems -- 3.7 Results of Numerical Experiments -- 4 Guaranteed Estimation of Parameters of Boundary Value Problems for Linear Ordinary Differential Equations with General Boundary Data -- 4.1 Auxiliary Results.
4.2 Statement of the Estimation Problem of Solutions -- 4.3 Representations for Minimax Estimates of the Values of Functionals -- 4.4 Minimax Estimation of Functionals from Right-Hand Sides -- 4.5 Minimax Estimation of Functionals from Solutions -- 4.6 Auxiliary Results -- 4.7 Statement of Estimation Problem -- 4.8 Theorems on the General form of Minimax Estimates -- 4.9 Estimation Problems of Functionals from Unknown Data -- References -- Index -- About the Authors -- Back Cover. |
| Record Nr. | UNINA-9910794628303321 |
Nakonechnyi O.
|
||
| Gistrup, Denmark ; ; London ; ; New York, New York : , : River Publishers : , : Routledge, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Guaranteed estimation problems in the theory of linear ordinary differential equations with uncertain data / / Oleksandr Nakonechnyi and Yuri Podlipenko
| Guaranteed estimation problems in the theory of linear ordinary differential equations with uncertain data / / Oleksandr Nakonechnyi and Yuri Podlipenko |
| Autore | Nakonechnyi O. |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Gistrup, Denmark ; ; London ; ; New York, New York : , : River Publishers : , : Routledge, , [2021] |
| Descrizione fisica | 1 online resource (234 pages) |
| Disciplina | 515.353 |
| Collana | River Publishers series in mathematical and engineering sciences |
| Soggetto topico |
Cauchy problem
Differential equations, Linear Estimation theory |
| ISBN |
1-00-333836-4
1-003-33836-4 1-000-79513-6 87-7022-631-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover -- Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data -- Contents -- Preface -- Introduction -- 1 Guaranteed Estimates of Solutions and Right-Hand Sides of the Cauchy Problem Under Incomplete Data -- 1.1 Preliminaries and Auxiliary Results -- 1.2 Statement of the Estimation Problem -- 1.3 Minimax Estimation of Functionals From Solutions of the Cauchy Problem -- 1.4 1-Optimal Estimates of Unknown Solution of the Cauchy Problem -- 1.5 Representations of Guaranteed Estimates of Functionals -- 1.6 Minimax Estimation of the Right-Hand Sides of Equalities that Enter -- 1.7 Guaranteed Estimation of Solutions to the Cauchy Problem -- 1.8 Guaranteed Predictive Estimation of Solutions to the Cauchy Problem -- 2 Guaranteed Estimation of Unknown Solutions and Right-Hand Sides of First Order Linear Systems of Periodic ODEs -- 2.1 Guaranteed Estimation of Solutions of First Order Linear Systems -- 2.2 Guaranteed Recovery of Unknown Right-Hand Sides -- 2.3 Guaranteed a Posteriori Estimation of Unknown Right-Hand Sides -- 3 Guaranteed Estimation of Solutions of Boundary Value Problems for Linear Ordinary Differential Equations with Decomposed Boundary Data -- 3.1 Preliminaries and Auxiliary Results -- 3.2 Statement of the Minimax Estimation Problem and Its Reduction -- 3.3 Representations for Minimax Estimates of Functionals from Solutions -- 3.4 Minimax Estimates of Solutions Subject to Incomplete Restrictions -- 3.5 Elimination Technique in Minimax Estimation Problems -- 3.6 Minimax Estimation of the Solutions to the Boundary Value Problems -- 3.7 Results of Numerical Experiments -- 4 Guaranteed Estimation of Parameters of Boundary Value Problems for Linear Ordinary Differential Equations with General Boundary Data -- 4.1 Auxiliary Results.
4.2 Statement of the Estimation Problem of Solutions -- 4.3 Representations for Minimax Estimates of the Values of Functionals -- 4.4 Minimax Estimation of Functionals from Right-Hand Sides -- 4.5 Minimax Estimation of Functionals from Solutions -- 4.6 Auxiliary Results -- 4.7 Statement of Estimation Problem -- 4.8 Theorems on the General form of Minimax Estimates -- 4.9 Estimation Problems of Functionals from Unknown Data -- References -- Index -- About the Authors -- Back Cover. |
| Record Nr. | UNINA-9910827488603321 |
|
Nakonechnyi O.
|
||
| Gistrup, Denmark ; ; London ; ; New York, New York : , : River Publishers : , : Routledge, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||