Computational methods for modelling of nonlinear systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
Elsevier
2007
|
| Ausgabe: | 1st ed |
| Schriftenreihe: | Mathematics in science and engineering
v. 212 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | 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 matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering Preface -- Contents -- 1 Overview -- I Methods of Operator Approximation in System Modelling -- 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 polynomial operators -- 2.5 Approximation on compact sets in topological vector spaces -- 2.6 Approximation on noncompact sets in Hilbert spaces -- 2.7 Special results for maps into Banach spaces -- 2.8 Concluding remarks -- 3 Interpolation of Nonlinear Operators 65 -- 3.1 Introduction -- 3.2 Lagrange interpolation in Banach spaces -- 3.3 Weak interpolation of nonlinear operators -- 3.4 Some related results -- 3.5 Concluding remarks -- 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 RŁcontinuous operators -- 4.4 Concluding remarks -- - 5 Methods of Best Approximation for Nonlinear Operators -- 5.1 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 polynomial approximation -- 5.6 Best causal approximation -- 5.7 Best hybrid approximations -- 5.8 Concluding remarks -- II Optimal Estimation of Random Vectors -- 6 Computational Methods for Optimal Filtering of Stochastic Signals -- 6.1 Introduction -- 6.2 Optimal linear Filtering in Finite dimensional vector spaces -- 6.3 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 -- 7 Computational Methods for Optimal Compression and -- Reconstruction of Random Data -- 7.1 Introduction -- - 7.2 Standard Principal Component Analysis and Karhunen-Loeeve transform (PCA{KLT) -- 7.3 Rank-constrained matrix approximations -- 7.4 Generic PCA{KLT -- 7.5 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 Includes bibliographical references (p. 379-393) and index |
| Beschreibung: | 1 Online-Ressource (xi, 397 p.) |
| ISBN: | 0080475388 0444530444 9780080475387 9780444530448 9780750668477 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043043927 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 151123s2007 |||| o||u| ||||||eng d | ||
| 020 | |a 0080475388 |c electronic bk. |9 0-08-047538-8 | ||
| 020 | |a 0444530444 |9 0-444-53044-4 | ||
| 020 | |a 9780080475387 |c electronic bk. |9 978-0-08-047538-7 | ||
| 020 | |a 9780444530448 |9 978-0-444-53044-8 | ||
| 020 | |a 9780750668477 |9 978-0-7506-6847-7 | ||
| 035 | |a (OCoLC)162131543 | ||
| 035 | |a (DE-599)BVBBV043043927 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1046 |a DE-1047 | ||
| 082 | 0 | |a 515.72480113 |2 22 | |
| 100 | 1 | |a Torokhti, A., (Anatoli) |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Computational methods for modelling of nonlinear systems |c A. Torokhti, P. Howlett |
| 246 | 1 | 3 | |a Computational methods for modeling of nonlinear systems |
| 250 | |a 1st ed | ||
| 264 | 1 | |a Amsterdam |b Elsevier |c 2007 | |
| 300 | |a 1 Online-Ressource (xi, 397 p.) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematics in science and engineering |v v. 212 | |
| 500 | |a 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 matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering | ||
| 500 | |a Preface -- Contents -- 1 Overview -- I Methods of Operator Approximation in System Modelling -- 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 polynomial operators -- 2.5 Approximation on compact sets in topological vector spaces -- 2.6 Approximation on noncompact sets in Hilbert spaces -- 2.7 Special results for maps into Banach spaces -- 2.8 Concluding remarks -- 3 Interpolation of Nonlinear Operators 65 -- 3.1 Introduction -- 3.2 Lagrange interpolation in Banach spaces -- 3.3 Weak interpolation of nonlinear operators -- 3.4 Some related results -- 3.5 Concluding remarks -- 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 RŁcontinuous operators -- 4.4 Concluding remarks -- | ||
| 500 | |a - 5 Methods of Best Approximation for Nonlinear Operators -- 5.1 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 polynomial approximation -- 5.6 Best causal approximation -- 5.7 Best hybrid approximations -- 5.8 Concluding remarks -- II Optimal Estimation of Random Vectors -- 6 Computational Methods for Optimal Filtering of Stochastic Signals -- 6.1 Introduction -- 6.2 Optimal linear Filtering in Finite dimensional vector spaces -- 6.3 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 -- 7 Computational Methods for Optimal Compression and -- Reconstruction of Random Data -- 7.1 Introduction -- | ||
| 500 | |a - 7.2 Standard Principal Component Analysis and Karhunen-Loeeve transform (PCA{KLT) -- 7.3 Rank-constrained matrix approximations -- 7.4 Generic PCA{KLT -- 7.5 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 | ||
| 500 | |a Includes bibliographical references (p. 379-393) and index | ||
| 650 | 7 | |a MATHEMATICS / Functional Analysis |2 bisacsh | |
| 650 | 7 | |a Niet-lineaire systemen |2 gtt | |
| 650 | 7 | |a Optimaliseren |2 gtt | |
| 650 | 7 | |a Nonlinear systems / Mathematical models |2 fast | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Nonlinear systems |x Mathematical models | |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematisches Modell |0 (DE-588)4114528-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineares System |0 (DE-588)4042110-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineares System |0 (DE-588)4042110-7 |D s |
| 689 | 0 | 1 | |a Mathematisches Modell |0 (DE-588)4114528-8 |D s |
| 689 | 0 | 2 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Howlett, P. G. |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=193629 |x Aggregator |3 Volltext |
| 912 | |a ZDB-4-EBA | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-028468465 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=193629 |l FAW01 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=193629 |l FAW02 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804175409201283072 |
|---|---|
| any_adam_object | |
| author | Torokhti, A., (Anatoli) |
| author_facet | Torokhti, A., (Anatoli) |
| author_role | aut |
| author_sort | Torokhti, A., (Anatoli) |
| author_variant | a a t aa aat |
| building | Verbundindex |
| bvnumber | BV043043927 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)162131543 (DE-599)BVBBV043043927 |
| dewey-full | 515.72480113 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.72480113 |
| dewey-search | 515.72480113 |
| dewey-sort | 3515.72480113 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1st ed |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06355nmm a2200637zcb4500</leader><controlfield tag="001">BV043043927</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">151123s2007 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0080475388</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">0-08-047538-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0444530444</subfield><subfield code="9">0-444-53044-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780080475387</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">978-0-08-047538-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780444530448</subfield><subfield code="9">978-0-444-53044-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780750668477</subfield><subfield code="9">978-0-7506-6847-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)162131543</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043043927</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-1046</subfield><subfield code="a">DE-1047</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.72480113</subfield><subfield code="2">22</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Torokhti, A., (Anatoli)</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Computational methods for modelling of nonlinear systems</subfield><subfield code="c">A. Torokhti, P. Howlett</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">Computational methods for modeling of nonlinear systems</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1st ed</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Amsterdam</subfield><subfield code="b">Elsevier</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xi, 397 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Mathematics in science and engineering</subfield><subfield code="v">v. 212</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">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 matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Preface -- Contents -- 1 Overview -- I Methods of Operator Approximation in System Modelling -- 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 polynomial operators -- 2.5 Approximation on compact sets in topological vector spaces -- 2.6 Approximation on noncompact sets in Hilbert spaces -- 2.7 Special results for maps into Banach spaces -- 2.8 Concluding remarks -- 3 Interpolation of Nonlinear Operators 65 -- 3.1 Introduction -- 3.2 Lagrange interpolation in Banach spaces -- 3.3 Weak interpolation of nonlinear operators -- 3.4 Some related results -- 3.5 Concluding remarks -- 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 RŁcontinuous operators -- 4.4 Concluding remarks -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 5 Methods of Best Approximation for Nonlinear Operators -- 5.1 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 polynomial approximation -- 5.6 Best causal approximation -- 5.7 Best hybrid approximations -- 5.8 Concluding remarks -- II Optimal Estimation of Random Vectors -- 6 Computational Methods for Optimal Filtering of Stochastic Signals -- 6.1 Introduction -- 6.2 Optimal linear Filtering in Finite dimensional vector spaces -- 6.3 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 -- 7 Computational Methods for Optimal Compression and -- Reconstruction of Random Data -- 7.1 Introduction -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 7.2 Standard Principal Component Analysis and Karhunen-Loeeve transform (PCA{KLT) -- 7.3 Rank-constrained matrix approximations -- 7.4 Generic PCA{KLT -- 7.5 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</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (p. 379-393) and index</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Functional Analysis</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Niet-lineaire systemen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Optimaliseren</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Nonlinear systems / Mathematical models</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematisches Modell</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nonlinear systems</subfield><subfield code="x">Mathematical models</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Numerisches Verfahren</subfield><subfield code="0">(DE-588)4128130-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematisches Modell</subfield><subfield code="0">(DE-588)4114528-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineares System</subfield><subfield code="0">(DE-588)4042110-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineares System</subfield><subfield code="0">(DE-588)4042110-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Mathematisches Modell</subfield><subfield code="0">(DE-588)4114528-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Numerisches Verfahren</subfield><subfield code="0">(DE-588)4128130-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Howlett, P. G.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=193629</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028468465</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=193629</subfield><subfield code="l">FAW01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=193629</subfield><subfield code="l">FAW02</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043043927 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:15:49Z |
| institution | BVB |
| isbn | 0080475388 0444530444 9780080475387 9780444530448 9780750668477 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028468465 |
| oclc_num | 162131543 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xi, 397 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Elsevier |
| record_format | marc |
| series2 | Mathematics in science and engineering |
| spelling | Torokhti, A., (Anatoli) Verfasser aut Computational methods for modelling of nonlinear systems A. Torokhti, P. Howlett Computational methods for modeling of nonlinear systems 1st ed Amsterdam Elsevier 2007 1 Online-Ressource (xi, 397 p.) txt rdacontent c rdamedia cr rdacarrier Mathematics in science and engineering v. 212 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 matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering Preface -- Contents -- 1 Overview -- I Methods of Operator Approximation in System Modelling -- 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 polynomial operators -- 2.5 Approximation on compact sets in topological vector spaces -- 2.6 Approximation on noncompact sets in Hilbert spaces -- 2.7 Special results for maps into Banach spaces -- 2.8 Concluding remarks -- 3 Interpolation of Nonlinear Operators 65 -- 3.1 Introduction -- 3.2 Lagrange interpolation in Banach spaces -- 3.3 Weak interpolation of nonlinear operators -- 3.4 Some related results -- 3.5 Concluding remarks -- 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 RŁcontinuous operators -- 4.4 Concluding remarks -- - 5 Methods of Best Approximation for Nonlinear Operators -- 5.1 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 polynomial approximation -- 5.6 Best causal approximation -- 5.7 Best hybrid approximations -- 5.8 Concluding remarks -- II Optimal Estimation of Random Vectors -- 6 Computational Methods for Optimal Filtering of Stochastic Signals -- 6.1 Introduction -- 6.2 Optimal linear Filtering in Finite dimensional vector spaces -- 6.3 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 -- 7 Computational Methods for Optimal Compression and -- Reconstruction of Random Data -- 7.1 Introduction -- - 7.2 Standard Principal Component Analysis and Karhunen-Loeeve transform (PCA{KLT) -- 7.3 Rank-constrained matrix approximations -- 7.4 Generic PCA{KLT -- 7.5 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 Includes bibliographical references (p. 379-393) and index MATHEMATICS / Functional Analysis bisacsh Niet-lineaire systemen gtt Optimaliseren gtt Nonlinear systems / Mathematical models fast Mathematisches Modell Nonlinear systems Mathematical models 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 1\p DE-604 Howlett, P. G. Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=193629 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Torokhti, A., (Anatoli) Computational methods for modelling of nonlinear systems MATHEMATICS / Functional Analysis bisacsh Niet-lineaire systemen gtt Optimaliseren gtt Nonlinear systems / Mathematical models fast Mathematisches Modell Nonlinear systems Mathematical models 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_alt | Computational methods for modeling 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 | MATHEMATICS / Functional Analysis bisacsh Niet-lineaire systemen gtt Optimaliseren gtt Nonlinear systems / Mathematical models fast Mathematisches Modell Nonlinear systems Mathematical models Numerisches Verfahren (DE-588)4128130-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Nichtlineares System (DE-588)4042110-7 gnd |
| topic_facet | MATHEMATICS / Functional Analysis Niet-lineaire systemen Optimaliseren Nonlinear systems / Mathematical models Mathematisches Modell Nonlinear systems Mathematical models Numerisches Verfahren Nichtlineares System |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=193629 |
| work_keys_str_mv | AT torokhtiaanatoli computationalmethodsformodellingofnonlinearsystems AT howlettpg computationalmethodsformodellingofnonlinearsystems AT torokhtiaanatoli computationalmethodsformodelingofnonlinearsystems AT howlettpg computationalmethodsformodelingofnonlinearsystems |