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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.
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.