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Guaranteed estimation problems in the theory of linear ordinary differential equations with uncertain data /
This monograph is devoted to the construction of optimal estimates of values of linear functionals on solutions to Cauchy and two-point boundary value problems for systems of linear first-order ordinary differential equations, from indirect observations which are linear transformations of the same s...
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Aalborg :
River Publishers,
2021.
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| Series: | River Publishers series in mathematical and engineering sciences
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| Subjects: | |
| Online Access: |
Full text (Wentworth users only) |
| Local Note: | ProQuest Ebook Central |
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| 100 | 1 | |a Nakonechnyĭ, O. H. |q (Oleksandr Hryhorovych) |1 https://id.oclc.org/worldcat/entity/E39PCjHvFkh48bQhJV6rc88R83 | |
| 245 | 1 | 0 | |a Guaranteed estimation problems in the theory of linear ordinary differential equations with uncertain data / |c Oleksandr Nakonechnyi, Yuri Podlipenko. |
| 264 | 1 | |a Aalborg : |b River Publishers, |c 2021. | |
| 300 | |a 1 online resource (234 pages) | ||
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| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a This monograph is devoted to the construction of optimal estimates of values of linear functionals on solutions to Cauchy and two-point boundary value problems for systems of linear first-order ordinary differential equations, from indirect observations which are linear transformations of the same solutions perturbed by additive random noises. | ||
| 545 | 0 | |a Oleksandr Nakonechnyi, Yuri Podlipenko | |
| 588 | 0 | |a Print version record. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Differential equations, Linear. | |
| 650 | 0 | |a Estimation theory. | |
| 650 | 0 | |a Cauchy problem. | |
| 650 | 0 | |a Probabilities. | |
| 650 | 7 | |a probability. |2 aat | |
| 700 | 1 | |a Podlipenko, Yuri, |e author. | |
| 776 | 0 | 8 | |i Print version: |a Nakonechnyi, Oleksandr. |t Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data. |d Aalborg : River Publishers, ©2021 |
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