LEADER 05096nam 2200661Ia 450 001 9910969695303321 005 20200520144314.0 010 $a9786611003906 010 $a9781281003904 010 $a1281003905 010 $a9780080475387 010 $a0080475388 035 $a(CKB)1000000000357664 035 $a(EBL)291694 035 $a(OCoLC)476050801 035 $a(PPN)170257843 035 $a(FR-PaCSA)41001463 035 $a(MiAaPQ)EBC291694 035 $a(FRCYB41001463)41001463 035 $a(EXLCZ)991000000000357664 100 $a20070206d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aComputational methods for modeling of nonlinear systems /$fA. Torokhti, P. Howlett 205 $a1st ed. 210 $aAmsterdam ;$aBoston $cElsevier$d2007 215 $a1 online resource (413 p.) 225 1 $aMathematics in science and engineering,$x0076-5392 ;$vv. 212 300 $aDescription based upon print version of record. 311 08$a9780444530448 311 08$a0444530444 320 $aIncludes bibliographical references (p. 379-393) and index. 327 $aFront Cover; Computational Methods for Modelling of Nonlinear Systems; Copyright Page; Preface; Table of Contents; Chapter 1 Overview; Part I Methods of Operator Approximation in System Modelling; Chapter 2 Nonlinear Operator Approximation with Preassigned Accuracy; 2.1 Introduction; 2.2 Generic Formulation of the Problem; 2.3 Operator Approximation in Space C([0, 1]); 2.4 Operator Approximation in Banach Spaces by Operator Polynomials; 2.5 Approximation on Compact Sets in Topological Vector Spaces; 2.6 Approximation on Noncompact Sets in Hilbert Spaces 327 $a2.7 Special Results for Maps into Banach Spaces2.8 Concluding Remarks; Chapter 3 Interpolation of Nonlinear Operators; 3.1 Introduction; 3.2 Lagrange Interpolation in Banach Spaces; 3.3 Weak Interpolation of Nonlinear Operators; 3.4 Strong interpolation; 3.5 Interpolation and approximation; 3.6 Some Related Results; 3.7 Concluding Remarks; Chapter 4 Realistic Operators and their Approximation; 4.1 Introduction; 4.2 Formalization of Concepts Related to Description of Real-World Objects; 4.3 Approximation of R-continuous Operators; 4.4 Concluding Remarks 327 $aChapter 5 Methods of Best Approximation for Nonlinear Operators5.1 Introduction; 5.2 Best Approximation of Nonlinear Operators in Banach Spaces: "Deterministic" Case; 5.3 Estimation of Mean and Covariance Matrix for Random Vectors; 5.4 Best Hadamard-quadratic Approximation; 5.5 Best r-Degree Polynomial Approximation; 5.6 Best Causal Approximation; 5.7 Best Hybrid Approximations; 5.8 Concluding Remarks; Part II Optimal Estimation of Random Vectors; Chapter 6 Computational Methods for Optimal Filtering of Stochastic Signals; 6.1 Introduction 327 $a6.2 Optimal Linear Filtering in Finite Dimensional Vector Spaces6.3 Optimal Linear Filtering in Hilbert Spaces; 6.4 Optimal Causal Linear Filtering with Piecewise Constant Memory; 6.5 Optimal Causal Polynomial Filtering with Arbitrarily Variable Memory; 6.6 Optimal Nonlinear Filtering with no Memory Constraint; 6.7 Concluding Remarks; Chapter 7 Computational Methods for Optimal Compression and Reconstruction of Random Data; 7.1 Introduction; 7.2 Standard Principal Component Analysis and Karhunen-Loe?ve Transform (PCA-KLT); 7.3 Rank-constrained Matrix Approximations 327 $a7.4 A Generic Principal Component Analysis and Karhunen-Loe?ve Transform7.5 Optimal Hybrid Transform Based on Hadamard-quadratic Approximation; 7.6 Optimal Transform Formed by a Combination of Nonlinear Operators; 7.7 Optimal Generalized Hybrid Transform; 7.8 Concluding Remarks; Bibliography; Index; Series Page 330 $aIn this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank 410 0$aMathematics in science and engineering ;$vv. 212. 606 $aSystem theory 606 $aNonlinear systems$xMathematical models 615 0$aSystem theory. 615 0$aNonlinear systems$xMathematical models. 676 $a515.72480113 676 $a515.72480113 686 $a31.80$2bcl 700 $aTorokhti$b A$g(Anatoli)$0307697 701 $aHowlett$b P. G$g(Philip G.),$f1944-$01796194 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910969695303321 996 $aComputational methods for modeling of nonlinear systems$94337863 997 $aUNINA