Computational methods for modelling of nonlinear systems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
2007
|
| Edition: | 1. ed. |
| Series: | Mathematics in science and engineering
212 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 397 S. Ill., graph. Darst. |
| ISBN: | 9780444530448 0444530444 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Preface
Contents
1 Overview
1 Methods of Operator Approximation in System Mod-
elling 7
2 Nonlinear Operator Approximation with Preassigned Ac-
curacy 9
2.1 Introduction........................... 9
2.2 Generic Formulation of the Problem.............. 10
2.3 Operator Approximation in Space C([0,1]).......... 11
2.4 Operator Approximation in Banach Spaces by Operator Poly-
nomials ............................. 13
2.5 Approximation on Compact Sets in Topological Vector Spaces 17
2.6 Approximation on Noncompact Sets in Hilbert Spaces ... 43
2.7 Special Results for Maps into Banach Spaces........ 59
2.8 Concluding Remarks...................... 62
3 Interpolation of Nonlinear Operators 65
3.1 Introduction........................... 65
3.2 Lagrange Interpolation in Banach Spaces .......... 66
3.3 Weak Interpolation of Nonlinear Operators ......... 74
3.4 Strong interpolation...................... 85
3.5 Interpolation and approximation............... 87
3.6 Some Related Results ..................... 94
3.7 Concluding Remarks...................... 95
x CONTENTS
4 Realistic Operators and their Approximation 97
4.1 Introduction........................... 97
4.2 Formalization of Concepts Related to Description of Real-
World Objects ......................... 99
4.3 Approximation of 7?.—continuous Operators......... 114
4.4 Concluding Remarks...................... 135
5 Methods of Best Approximation for Nonlinear Operators 137
5.1 Introduction........................... 137
5.2 Best Approximation of Nonlinear Operators in Banach Spaces:
Deterministic Case...................... 139
5.3 Estimation of Mean and Covariance Matrix for Random Vec-
tors ............................... 146
5.4 Best Hadamard-quadratic Approximation.......... 165
5.5 Best r-Degree Polynomial Approximation.......... 178
5.6 Best Causal Approximation.................. 198
5.7 Best Hybrid Approximations ................. 210
5.8 Concluding Remarks...................... 225
II Optimal Estimation of Random Vectors 227
6 Computational Methods for Optimal Filtering of Stochas-
tic Signals 229
6.1 Introduction........................... 229
6.2 Optimal Linear Filtering in Finite Dimensional Vector Spaces230
6.3 Optimal Linear Filtering in Hilbert Spaces.......... 231
6.4 Optimal Causal Linear Filtering with Piecewise Constant
Memory............................. 248
6.5 Optimal Causal Polynomial Filtering with Arbitrarily Vari-
able Memory.......................... 265
6.6 Optimal Nonlinear Filtering with no Memory Constraint . . 284
6.7 Concluding Remarks...................... 290
7 Computational Methods for Optimal Compression and
Reconstruction of Random Data 291
7.1 Introduction........................... 291
7.2 Standard Principal Component Analysis and Karhunen-Loeve
Transform (PCA-KLT) .................... 293
7.3 Rank-constrained Matrix Approximations.......... 294
7.4 A Generic Principal Component Analysis and Karhunen-
Loeve Transform........................ 309
CONTENTS xi
7.5 Optimal Hybrid Transform Based on Hadamard-quadratic
Approximation......................... 315
7.6 Optimal Transform Formed by a Combination of Nonlinear
Operators............................ 338
7.7 Optimal Generalized Hybrid Transform ........... 373
7.8 Concluding Remarks...................... 377
Bibliography 379
Index 395
|
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| id | DE-604.BV025494708 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:35:19Z |
| institution | BVB |
| isbn | 9780444530448 0444530444 |
| language | English |
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| physical | XI, 397 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Elsevier |
| record_format | marc |
| series | Mathematics in science and engineering |
| series2 | Mathematics in science and engineering |
| spelling | Torokhti, Anatoli Verfasser aut Computational methods for modelling of nonlinear systems A. Torokhti ; P. Howlett 1. ed. Amsterdam [u.a.] Elsevier 2007 XI, 397 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics in science and engineering 212 Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Nichtlineares System (DE-588)4042110-7 gnd rswk-swf Nichtlineares System (DE-588)4042110-7 s Mathematisches Modell (DE-588)4114528-8 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Howlett, Phil Verfasser aut Mathematics in science and engineering 212 (DE-604)BV000001196 212 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020106955&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Torokhti, Anatoli Howlett, Phil Computational methods for modelling of nonlinear systems Mathematics in science and engineering Numerisches Verfahren (DE-588)4128130-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Nichtlineares System (DE-588)4042110-7 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4114528-8 (DE-588)4042110-7 |
| title | Computational methods for modelling of nonlinear systems |
| title_auth | Computational methods for modelling of nonlinear systems |
| title_exact_search | Computational methods for modelling of nonlinear systems |
| title_full | Computational methods for modelling of nonlinear systems A. Torokhti ; P. Howlett |
| title_fullStr | Computational methods for modelling of nonlinear systems A. Torokhti ; P. Howlett |
| title_full_unstemmed | Computational methods for modelling of nonlinear systems A. Torokhti ; P. Howlett |
| title_short | Computational methods for modelling of nonlinear systems |
| title_sort | computational methods for modelling of nonlinear systems |
| topic | Numerisches Verfahren (DE-588)4128130-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Nichtlineares System (DE-588)4042110-7 gnd |
| topic_facet | Numerisches Verfahren Mathematisches Modell Nichtlineares System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020106955&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001196 |
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