LEADER 04638nam 22005293u 450 001 9910457243503321 005 20210114050116.0 010 $a1-281-00390-5 010 $a9786611003906 010 $a0-08-047538-8 035 $a(CKB)1000000000357664 035 $a(EBL)291694 035 $a(OCoLC)476050801 035 $a(MiAaPQ)EBC291694 035 $a(PPN)170257843 035 $a(EXLCZ)991000000000357664 100 $a20140113d2007|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 200 10$aComputational Methods for Modeling of Nonlinear Systems$b[electronic resource] 210 $aBurlington $cElsevier Science$d2007 215 $a1 online resource (413 p.) 225 1 $aMathematics in science and engineering 300 $aDescription based upon print version of record. 311 $a0-444-53044-4 327 $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 606 $aMathematical models 606 $aNonlinear systems 608 $aElectronic books. 615 4$aMathematical models. 615 4$aNonlinear systems. 676 $a515.72480113 700 $aTorokhti$b Anatoli$0307697 701 $aHowlett$b Phil$0429754 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a9910457243503321 996 $aComputational Methods for Modeling of Nonlinear Systems$92167210 997 $aUNINA LEADER 01616nam 22004093 450 001 996678669903316 005 20251001080513.0 010 $a3-032-06085-0 035 $a(CKB)41082241400041 035 $a(MiAaPQ)EBC32321600 035 $a(Au-PeEL)EBL32321600 035 $a(OCoLC)1543209518 035 $a(EXLCZ)9941082241400041 100 $a20251001d2025 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAutomated Reasoning with Analytic Tableaux and Related Methods $e34th International Conference, TABLEAUX 2025, Reykjavik, Iceland, September 27-29, 2025, Proceedings 205 $a1st ed. 210 1$aCham :$cSpringer,$d2025. 210 4$dİ2026. 215 $a1 online resource (968 pages) 225 1 $aLecture Notes in Computer Science Series ;$vv.15980 311 08$a3-032-06084-2 330 $aThis open access book constitutes the proceedings of the 33rd International Conference on Automated Reasoning with AnalyticTableaux and Related Methods, TABLEAUX 2025, held in Reykjavik, Iceland, during September 27-29, 2025.The 25 full papers included in this book were carefully reviewed and selected from 47 sbumissions. 410 0$aLecture Notes in Computer Science Series 700 $aPozzato$b Gian Luca$01849991 701 $aUustalu$b Tarmo$01754880 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996678669903316 996 $aAutomated Reasoning with Analytic Tableaux and Related Methods$94442739 997 $aUNISA