{"text_format":"2","workbook":"xls","n_sheets":1,"sheets":["report2"],"not_rendered":{"charts":0,"images":0,"macros":0,"external_links":1,"defined_names":1,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"run_cost":"one","rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"report2","index":0,"n_rows":24,"n_cols":5,"rows_kept":24,"cut":false,"hidden":false,"merged":[[0,2,0,3],[0,4,0,5],[1,2,1,3],[1,4,1,5],[2,2,2,3],[2,4,2,5],[3,2,3,3],[4,2,4,3],[7,2,7,3],[8,2,8,3],[9,2,9,3],[10,2,10,3],[13,2,13,3],[14,2,14,3],[17,2,17,3]],"flags":["formulas_cached_only"]}
[null,"1.","Record Nr.",null,"UNINA9910457243503321"]
[null,null,"Autore",null,"Torokhti Anatoli"]
[null,null,"Titolo",null,"Computational Methods for Modeling of Nonlinear Systems [[electronic resource]]"]
[null,null,"Pubbl/distr/stampa",null,"Burlington, : Elsevier Science, 2007"]
[null,null,"ISBN",null,"1-281-00390-5"]
[{"$nulls":4},"9786611003906"]
[{"$nulls":4},"0-08-047538-8"]
[null,null,"Descrizione fisica",null,"1 online resource (413 p.)"]
[null,null,"Collana",null,"Mathematics in science and engineering"]
[null,null,"Disciplina",null,"515.72480113"]
[null,null,"Soggetti",null,"Mathematical models"]
[{"$nulls":4},"Nonlinear systems"]
[{"$nulls":4},"Electronic books."]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,"Nota di contenuto",null,"Front 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"]
[{"$nulls":4},"2.7 Special Results for Maps into Banach Spaces2.8 Concluding Remarks; Chapter 3 Interpolation of Nonlinear Operators; 3.1 Introduction; 3.2 Lagrange Interpolation in Banach Spaces; 3.3 Weak Interpolation of Nonlinear Operators; 3.4 Strong interpolation; 3.5 Interpolation and approximation; 3.6 Some Related Results; 3.7 Concluding Remarks; Chapter 4 Realistic Operators and their Approximation; 4.1 Introduction; 4.2 Formalization of Concepts Related to Description of Real-World Objects; 4.3 Approximation of R-continuous Operators; 4.4 Concluding Remarks"]
[{"$nulls":4},"Chapter 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 "]
[{"$nulls":4},"Approximation; 5.5 Best r-Degree Polynomial Approximation; 5.6 Best Causal Approximation; 5.7 Best Hybrid Approximations; 5.8 Concluding Remarks; Part II Optimal Estimation of Random Vectors; Chapter 6 Computational Methods for Optimal Filtering of Stochastic Signals; 6.1 Introduction"]
[{"$nulls":4},"6.2 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-Loève Transform (PCA-KLT); 7.3 Rank-constrained Matrix Approximations"]
[{"$nulls":4},"7.4 A Generic Principal Component Analysis and Karhunen-Loève 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"]
[null,null,null,"Sommario/riassunto","In 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"]