Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems
We propose a posteriori error bounds for reduced-order models of non-parametrized linear time invariant (LTI) systems and parametrized LTI systems. The error bounds estimate the errors of the transfer functions of the reduced-order models, and are independent of the model reduction methods used. It...
Gespeichert in:
| Veröffentlicht in: | ESAIM. Mathematical modelling and numerical analysis 2017-11, Vol.51 (6), p.2127-2158 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 2158 |
|---|---|
| container_issue | 6 |
| container_start_page | 2127 |
| container_title | ESAIM. Mathematical modelling and numerical analysis |
| container_volume | 51 |
| creator | Feng, Lihong Antoulas, Athanasios C. Benner, Peter |
| description | We propose a posteriori error bounds for reduced-order models of non-parametrized linear time invariant (LTI) systems and parametrized LTI systems. The error bounds estimate the errors of the transfer functions of the reduced-order models, and are independent of the model reduction methods used. It is shown that for some special non-parametrized LTI systems, particularly efficiently computable error bounds can be derived. According to the error bounds, reduced-order models of both non-parametrized and parametrized systems, computed by Krylov subspace based model reduction methods, can be obtained automatically and reliably. Simulations for several examples from engineering applications have demonstrated the robustness of the error bounds. |
| doi_str_mv | 10.1051/m2an/2017014 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2199218377</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2199218377</sourcerecordid><originalsourceid>FETCH-LOGICAL-c301t-9a3c74442e4c94770a74afe5d8222ed4a5f7dcf6a2de818c8e1817e7d47e91473</originalsourceid><addsrcrecordid>eNo9kNFKwzAUhoMoOKd3PkDAGwXjkjRt0ksRN4UxEZV5F2JzKp1rU09acD69HRtenR_Ox384HyHngt8InopJLV0zkVxoLtQBGQmZc5YYJQ7JiOtMsdQk78fkJMYV51xwlY6IfQk1UEfbEDvAKmBFATEg_Qh94yMth4jg-wI8C-gBaR08rNdV80lDSS-b0LCr1qGrocPqFzwdVuCQxs1QWMdTclS6dYSz_RyTt-n9690Dmz_NHu9u56xIuOhY7pJCK6UkqCJXWnOnlSsh9UZKCV65tNS-KDMnPRhhCgPCCA3aKw25UDoZk4tdb4vhu4fY2VXosRlOWinyXAqT6C11vaMKDDEilLbFqna4sYLbrUK7VWj3Cgec7fBq-OXnn3X4ZTOd6NQavrSz-XSxfJ5ndpH8AeIzdBg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2199218377</pqid></control><display><type>article</type><title>Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems</title><source>Alma/SFX Local Collection</source><creator>Feng, Lihong ; Antoulas, Athanasios C. ; Benner, Peter</creator><creatorcontrib>Feng, Lihong ; Antoulas, Athanasios C. ; Benner, Peter</creatorcontrib><description>We propose a posteriori error bounds for reduced-order models of non-parametrized linear time invariant (LTI) systems and parametrized LTI systems. The error bounds estimate the errors of the transfer functions of the reduced-order models, and are independent of the model reduction methods used. It is shown that for some special non-parametrized LTI systems, particularly efficiently computable error bounds can be derived. According to the error bounds, reduced-order models of both non-parametrized and parametrized systems, computed by Krylov subspace based model reduction methods, can be obtained automatically and reliably. Simulations for several examples from engineering applications have demonstrated the robustness of the error bounds.</description><identifier>ISSN: 0764-583X</identifier><identifier>EISSN: 1290-3841</identifier><identifier>DOI: 10.1051/m2an/2017014</identifier><language>eng</language><publisher>Les Ulis: EDP Sciences</publisher><subject>37M05 ; 65L70 ; 65L80 ; 65P99 ; Computer simulation ; error estimation ; Error reduction ; Linear systems ; Model order reduction ; Model reduction ; Parameterization ; Reduced order models ; Subspace methods ; Transfer functions</subject><ispartof>ESAIM. Mathematical modelling and numerical analysis, 2017-11, Vol.51 (6), p.2127-2158</ispartof><rights>2017. Notwithstanding the ProQuest Terms and conditions, you may use this content in accordance with the associated terms available at https://www.esaim-m2an.org/articles/m2an/abs/2017/06/m2an160008/m2an160008.html .</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c301t-9a3c74442e4c94770a74afe5d8222ed4a5f7dcf6a2de818c8e1817e7d47e91473</citedby><cites>FETCH-LOGICAL-c301t-9a3c74442e4c94770a74afe5d8222ed4a5f7dcf6a2de818c8e1817e7d47e91473</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Feng, Lihong</creatorcontrib><creatorcontrib>Antoulas, Athanasios C.</creatorcontrib><creatorcontrib>Benner, Peter</creatorcontrib><title>Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems</title><title>ESAIM. Mathematical modelling and numerical analysis</title><description>We propose a posteriori error bounds for reduced-order models of non-parametrized linear time invariant (LTI) systems and parametrized LTI systems. The error bounds estimate the errors of the transfer functions of the reduced-order models, and are independent of the model reduction methods used. It is shown that for some special non-parametrized LTI systems, particularly efficiently computable error bounds can be derived. According to the error bounds, reduced-order models of both non-parametrized and parametrized systems, computed by Krylov subspace based model reduction methods, can be obtained automatically and reliably. Simulations for several examples from engineering applications have demonstrated the robustness of the error bounds.</description><subject>37M05</subject><subject>65L70</subject><subject>65L80</subject><subject>65P99</subject><subject>Computer simulation</subject><subject>error estimation</subject><subject>Error reduction</subject><subject>Linear systems</subject><subject>Model order reduction</subject><subject>Model reduction</subject><subject>Parameterization</subject><subject>Reduced order models</subject><subject>Subspace methods</subject><subject>Transfer functions</subject><issn>0764-583X</issn><issn>1290-3841</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNo9kNFKwzAUhoMoOKd3PkDAGwXjkjRt0ksRN4UxEZV5F2JzKp1rU09acD69HRtenR_Ox384HyHngt8InopJLV0zkVxoLtQBGQmZc5YYJQ7JiOtMsdQk78fkJMYV51xwlY6IfQk1UEfbEDvAKmBFATEg_Qh94yMth4jg-wI8C-gBaR08rNdV80lDSS-b0LCr1qGrocPqFzwdVuCQxs1QWMdTclS6dYSz_RyTt-n9690Dmz_NHu9u56xIuOhY7pJCK6UkqCJXWnOnlSsh9UZKCV65tNS-KDMnPRhhCgPCCA3aKw25UDoZk4tdb4vhu4fY2VXosRlOWinyXAqT6C11vaMKDDEilLbFqna4sYLbrUK7VWj3Cgec7fBq-OXnn3X4ZTOd6NQavrSz-XSxfJ5ndpH8AeIzdBg</recordid><startdate>20171101</startdate><enddate>20171101</enddate><creator>Feng, Lihong</creator><creator>Antoulas, Athanasios C.</creator><creator>Benner, Peter</creator><general>EDP Sciences</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20171101</creationdate><title>Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems</title><author>Feng, Lihong ; Antoulas, Athanasios C. ; Benner, Peter</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c301t-9a3c74442e4c94770a74afe5d8222ed4a5f7dcf6a2de818c8e1817e7d47e91473</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>37M05</topic><topic>65L70</topic><topic>65L80</topic><topic>65P99</topic><topic>Computer simulation</topic><topic>error estimation</topic><topic>Error reduction</topic><topic>Linear systems</topic><topic>Model order reduction</topic><topic>Model reduction</topic><topic>Parameterization</topic><topic>Reduced order models</topic><topic>Subspace methods</topic><topic>Transfer functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Feng, Lihong</creatorcontrib><creatorcontrib>Antoulas, Athanasios C.</creatorcontrib><creatorcontrib>Benner, Peter</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>ESAIM. Mathematical modelling and numerical analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Feng, Lihong</au><au>Antoulas, Athanasios C.</au><au>Benner, Peter</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems</atitle><jtitle>ESAIM. Mathematical modelling and numerical analysis</jtitle><date>2017-11-01</date><risdate>2017</risdate><volume>51</volume><issue>6</issue><spage>2127</spage><epage>2158</epage><pages>2127-2158</pages><issn>0764-583X</issn><eissn>1290-3841</eissn><abstract>We propose a posteriori error bounds for reduced-order models of non-parametrized linear time invariant (LTI) systems and parametrized LTI systems. The error bounds estimate the errors of the transfer functions of the reduced-order models, and are independent of the model reduction methods used. It is shown that for some special non-parametrized LTI systems, particularly efficiently computable error bounds can be derived. According to the error bounds, reduced-order models of both non-parametrized and parametrized systems, computed by Krylov subspace based model reduction methods, can be obtained automatically and reliably. Simulations for several examples from engineering applications have demonstrated the robustness of the error bounds.</abstract><cop>Les Ulis</cop><pub>EDP Sciences</pub><doi>10.1051/m2an/2017014</doi><tpages>32</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0764-583X |
| ispartof | ESAIM. Mathematical modelling and numerical analysis, 2017-11, Vol.51 (6), p.2127-2158 |
| issn | 0764-583X 1290-3841 |
| language | eng |
| recordid | cdi_proquest_journals_2199218377 |
| source | Alma/SFX Local Collection |
| subjects | 37M05 65L70 65L80 65P99 Computer simulation error estimation Error reduction Linear systems Model order reduction Model reduction Parameterization Reduced order models Subspace methods Transfer functions |
| title | Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-06T20%3A55%3A06IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Some%20a%20posteriori%20error%20bounds%20for%20reduced-order%20modelling%20of%20(non-)parametrized%20linear%20systems&rft.jtitle=ESAIM.%20Mathematical%20modelling%20and%20numerical%20analysis&rft.au=Feng,%20Lihong&rft.date=2017-11-01&rft.volume=51&rft.issue=6&rft.spage=2127&rft.epage=2158&rft.pages=2127-2158&rft.issn=0764-583X&rft.eissn=1290-3841&rft_id=info:doi/10.1051/m2an/2017014&rft_dat=%3Cproquest_cross%3E2199218377%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2199218377&rft_id=info:pmid/&rfr_iscdi=true |