LEADER 04588nam 2200589 450 001 9910827488603321 005 20230117000348.0 010 $a1-00-333836-4 010 $a1-003-33836-4 010 $a1-000-79513-6 010 $a87-7022-631-8 035 $a(CKB)4100000012162987 035 $a(MiAaPQ)EBC29002964 035 $a(Au-PeEL)EBL29002964 035 $a(OCoLC)1290484482 035 $a(MiAaPQ)EBC7078874 035 $a(Au-PeEL)EBL7078874 035 $a(EXLCZ)994100000012162987 100 $a20230117d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGuaranteed estimation problems in the theory of linear ordinary differential equations with uncertain data /$fOleksandr Nakonechnyi and Yuri Podlipenko 205 $a1st ed. 210 1$aGistrup, Denmark ;$aLondon ;$aNew York, New York :$cRiver Publishers :$cRoutledge,$d[2021] 210 4$dİ2021 215 $a1 online resource (234 pages) 225 0 $aRiver Publishers series in mathematical and engineering sciences 311 $a87-7022-632-6 320 $aIncludes bibliographical references and index. 327 $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. 327 $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. 330 $aThis monograph is devoted to the construction of optimal estimates of values of linear functionals on solutions to Cauchy and two-point boundary value problems for systems of linear first-order ordinary differential equations, from indirect observations which are linear transformations of the same solutions perturbed by additive random noises. 410 0$aRiver Publishers Series in Mathematical and Engineering Sciences 606 $aCauchy problem 606 $aDifferential equations, Linear 606 $aEstimation theory 615 0$aCauchy problem. 615 0$aDifferential equations, Linear. 615 0$aEstimation theory. 676 $a515.353 700 $aNakonechnyi$b O.$01719495 702 $aPodlipenko$b Yuri 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827488603321 996 $aGuaranteed estimation problems in the theory of linear ordinary differential equations with uncertain data$94117379 997 $aUNINA