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001456398 1001_ $$aNakonechnyi, Oleksandr.
001456398 24510 $$aGuaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data.
001456398 250__ $$a1st ed.
001456398 264_1 $$aAalborg :$$bRiver Publishers,$$c2021.
001456398 264_4 $$c©2021.
001456398 300__ $$a1 online resource (234 pages).
001456398 336__ $$atext$$btxt$$2rdacontent
001456398 337__ $$acomputer$$bc$$2rdamedia
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001456398 5050_ $$aFront Cover -- Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data -- Contents -- Preface -- Introduction -- 1 Guaranteed Estimates of Solutions and Right-Hand Sides of the Cauchy Problem Under Incomplete Data -- 1.1 Preliminaries and Auxiliary Results -- 1.2 Statement of the Estimation Problem -- 1.3 Minimax Estimation of Functionals From Solutions of the Cauchy Problem -- 1.4 1-Optimal Estimates of Unknown Solution of the Cauchy Problem -- 1.5 Representations of Guaranteed Estimates of Functionals -- 1.6 Minimax Estimation of the Right-Hand Sides of Equalities that Enter -- 1.7 Guaranteed Estimation of Solutions to the Cauchy Problem -- 1.8 Guaranteed Predictive Estimation of Solutions to the Cauchy Problem -- 2 Guaranteed Estimation of Unknown Solutions and Right-Hand Sides of First Order Linear Systems of Periodic ODEs -- 2.1 Guaranteed Estimation of Solutions of First Order Linear Systems -- 2.2 Guaranteed Recovery of Unknown Right-Hand Sides -- 2.3 Guaranteed a Posteriori Estimation of Unknown Right-Hand Sides -- 3 Guaranteed Estimation of Solutions of Boundary Value Problems for Linear Ordinary Differential Equations with Decomposed Boundary Data -- 3.1 Preliminaries and Auxiliary Results -- 3.2 Statement of the Minimax Estimation Problem and Its Reduction -- 3.3 Representations for Minimax Estimates of Functionals from Solutions -- 3.4 Minimax Estimates of Solutions Subject to Incomplete Restrictions -- 3.5 Elimination Technique in Minimax Estimation Problems -- 3.6 Minimax Estimation of the Solutions to the Boundary Value Problems -- 3.7 Results of Numerical Experiments -- 4 Guaranteed Estimation of Parameters of Boundary Value Problems for Linear Ordinary Differential Equations with General Boundary Data -- 4.1 Auxiliary Results.
001456398 5058_ $$a4.2 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.
001456398 506__ $$aAccess limited to authorized users.
001456398 520__ $$aThis 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.
001456398 588__ $$aDescription based on publisher supplied metadata and other sources.
001456398 650_0 $$aDifferential equations, Linear.
001456398 650_0 $$aEstimation theory.
001456398 650_0 $$aProbabilities.
001456398 655_0 $$aElectronic books
001456398 77608 $$iPrint version:$$aNakonechnyi, Oleksandr$$tGuaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data$$dAalborg : River Publishers,c2021
001456398 852__ $$bebk
001456398 85640 $$3ProQuest Ebook Central Academic Complete $$uhttps://univsouthin.idm.oclc.org/login?url=https://ebookcentral.proquest.com/lib/usiricelib-ebooks/detail.action?docID=29002964$$zOnline Access
001456398 909CO $$ooai:library.usi.edu:1456398$$pGLOBAL_SET
001456398 980__ $$aBIB
001456398 980__ $$aEBOOK
001456398 982__ $$aEbook
001456398 983__ $$aOnline