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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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Nakonechnyĭ, O. H. (Oleksandr Hryhorovych), Podlipenko, Yuri (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Aalborg : River Publishers, 2021.
Colección:River Publishers series in mathematical and engineering sciences
Temas:
Differential equations, Linear.
Estimation theory.
Cauchy problem.
Probabilities.
Équations différentielles linéaires.
Théorie de l'estimation.
Problème de Cauchy.
Probabilités.
probability.
SCIENCE > Energy.
Probabilities
Cauchy problem
Differential equations, Linear
Estimation theory
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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