Explicit Bounds for the Pseudospectra of Various Classes of Matrices and Operators
We study the \(\epsilon\)-pseudospectra \(\sigma_\epsilon(A)\) of square matrices \(A \in \mathbb{C}^{N \times N}\). We give a complete characterization of the \(\epsilon\)-pseudospectrum of any \(2 \times 2\) matrix and describe the asymptotic behavior (as \(\epsilon \to 0\)) of \(\sigma_\epsilon(A...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2015-05 |
|---|---|
| Hauptverfasser: | , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | Gong, Feixue Meyerson, Olivia Meza, Jeremy Stoiciu, Mihai Ward, Abigail |
| description | We study the \(\epsilon\)-pseudospectra \(\sigma_\epsilon(A)\) of square matrices \(A \in \mathbb{C}^{N \times N}\). We give a complete characterization of the \(\epsilon\)-pseudospectrum of any \(2 \times 2\) matrix and describe the asymptotic behavior (as \(\epsilon \to 0\)) of \(\sigma_\epsilon(A)\) for any square matrix \(A\). We also present explicit upper and lower bounds for the \(\epsilon\)-pseudospectra of bidiagonal matrices, as well as for finite rank operators. |
| doi_str_mv | 10.48550/arxiv.1505.05931 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_1505_05931</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2078951875</sourcerecordid><originalsourceid>FETCH-LOGICAL-a525-48a4763021be1d3a40ebeb5c9af0456d280ce39a82744407cf2323c07df889c73</originalsourceid><addsrcrecordid>eNotj09Lw0AUxBdBsNR-AE8ueE59--d1N0ct1QqVihSv4XWzwZTYjbuJ1G9v2nqaYRiG-TF2I2CqLSLcUzzUP1OBgFPAXIkLNpJKicxqKa_YJKUdAMiZkYhqxN4Xh7apXd3xx9Dvy8SrEHn36flb8n0ZUutdF4mHin9QrEOf-LyhlHw6Rq_UxdoNnvYlX7c-UhdiumaXFTXJT_51zDZPi818ma3Wzy_zh1VGKDHTlrSZKZBi60WpSIPf-i26nCrQOCulBedVTlYarTUYV0kllQNTVtbmzqgxuz3PnoCLNtZfFH-LI3hxAh8ad-dGG8N371NX7EIf98OnQoKxOQprUP0B-rxa2w</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2078951875</pqid></control><display><type>article</type><title>Explicit Bounds for the Pseudospectra of Various Classes of Matrices and Operators</title><source>arXiv.org</source><source>Free E- Journals</source><creator>Gong, Feixue ; Meyerson, Olivia ; Meza, Jeremy ; Stoiciu, Mihai ; Ward, Abigail</creator><creatorcontrib>Gong, Feixue ; Meyerson, Olivia ; Meza, Jeremy ; Stoiciu, Mihai ; Ward, Abigail</creatorcontrib><description>We study the \(\epsilon\)-pseudospectra \(\sigma_\epsilon(A)\) of square matrices \(A \in \mathbb{C}^{N \times N}\). We give a complete characterization of the \(\epsilon\)-pseudospectrum of any \(2 \times 2\) matrix and describe the asymptotic behavior (as \(\epsilon \to 0\)) of \(\sigma_\epsilon(A)\) for any square matrix \(A\). We also present explicit upper and lower bounds for the \(\epsilon\)-pseudospectra of bidiagonal matrices, as well as for finite rank operators.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1505.05931</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Asymptotic properties ; Lower bounds ; Mathematics - Numerical Analysis ; Mathematics - Spectral Theory ; Operators (mathematics)</subject><ispartof>arXiv.org, 2015-05</ispartof><rights>2015. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,780,881,27902</link.rule.ids><backlink>$$Uhttps://doi.org/10.48550/arXiv.1505.05931$$DView paper in arXiv$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.2140/involve.2016.9.517$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink></links><search><creatorcontrib>Gong, Feixue</creatorcontrib><creatorcontrib>Meyerson, Olivia</creatorcontrib><creatorcontrib>Meza, Jeremy</creatorcontrib><creatorcontrib>Stoiciu, Mihai</creatorcontrib><creatorcontrib>Ward, Abigail</creatorcontrib><title>Explicit Bounds for the Pseudospectra of Various Classes of Matrices and Operators</title><title>arXiv.org</title><description>We study the \(\epsilon\)-pseudospectra \(\sigma_\epsilon(A)\) of square matrices \(A \in \mathbb{C}^{N \times N}\). We give a complete characterization of the \(\epsilon\)-pseudospectrum of any \(2 \times 2\) matrix and describe the asymptotic behavior (as \(\epsilon \to 0\)) of \(\sigma_\epsilon(A)\) for any square matrix \(A\). We also present explicit upper and lower bounds for the \(\epsilon\)-pseudospectra of bidiagonal matrices, as well as for finite rank operators.</description><subject>Asymptotic properties</subject><subject>Lower bounds</subject><subject>Mathematics - Numerical Analysis</subject><subject>Mathematics - Spectral Theory</subject><subject>Operators (mathematics)</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><sourceid>GOX</sourceid><recordid>eNotj09Lw0AUxBdBsNR-AE8ueE59--d1N0ct1QqVihSv4XWzwZTYjbuJ1G9v2nqaYRiG-TF2I2CqLSLcUzzUP1OBgFPAXIkLNpJKicxqKa_YJKUdAMiZkYhqxN4Xh7apXd3xx9Dvy8SrEHn36flb8n0ZUutdF4mHin9QrEOf-LyhlHw6Rq_UxdoNnvYlX7c-UhdiumaXFTXJT_51zDZPi818ma3Wzy_zh1VGKDHTlrSZKZBi60WpSIPf-i26nCrQOCulBedVTlYarTUYV0kllQNTVtbmzqgxuz3PnoCLNtZfFH-LI3hxAh8ad-dGG8N371NX7EIf98OnQoKxOQprUP0B-rxa2w</recordid><startdate>20150522</startdate><enddate>20150522</enddate><creator>Gong, Feixue</creator><creator>Meyerson, Olivia</creator><creator>Meza, Jeremy</creator><creator>Stoiciu, Mihai</creator><creator>Ward, Abigail</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PHGZM</scope><scope>PHGZT</scope><scope>PIMPY</scope><scope>PKEHL</scope><scope>PQEST</scope><scope>PQGLB</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20150522</creationdate><title>Explicit Bounds for the Pseudospectra of Various Classes of Matrices and Operators</title><author>Gong, Feixue ; Meyerson, Olivia ; Meza, Jeremy ; Stoiciu, Mihai ; Ward, Abigail</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a525-48a4763021be1d3a40ebeb5c9af0456d280ce39a82744407cf2323c07df889c73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Asymptotic properties</topic><topic>Lower bounds</topic><topic>Mathematics - Numerical Analysis</topic><topic>Mathematics - Spectral Theory</topic><topic>Operators (mathematics)</topic><toplevel>online_resources</toplevel><creatorcontrib>Gong, Feixue</creatorcontrib><creatorcontrib>Meyerson, Olivia</creatorcontrib><creatorcontrib>Meza, Jeremy</creatorcontrib><creatorcontrib>Stoiciu, Mihai</creatorcontrib><creatorcontrib>Ward, Abigail</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest Central (New)</collection><collection>ProQuest One Academic (New)</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Middle East (New)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Applied & Life Sciences</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gong, Feixue</au><au>Meyerson, Olivia</au><au>Meza, Jeremy</au><au>Stoiciu, Mihai</au><au>Ward, Abigail</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Explicit Bounds for the Pseudospectra of Various Classes of Matrices and Operators</atitle><jtitle>arXiv.org</jtitle><date>2015-05-22</date><risdate>2015</risdate><eissn>2331-8422</eissn><abstract>We study the \(\epsilon\)-pseudospectra \(\sigma_\epsilon(A)\) of square matrices \(A \in \mathbb{C}^{N \times N}\). We give a complete characterization of the \(\epsilon\)-pseudospectrum of any \(2 \times 2\) matrix and describe the asymptotic behavior (as \(\epsilon \to 0\)) of \(\sigma_\epsilon(A)\) for any square matrix \(A\). We also present explicit upper and lower bounds for the \(\epsilon\)-pseudospectra of bidiagonal matrices, as well as for finite rank operators.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1505.05931</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2015-05 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_arxiv_primary_1505_05931 |
| source | arXiv.org; Free E- Journals |
| subjects | Asymptotic properties Lower bounds Mathematics - Numerical Analysis Mathematics - Spectral Theory Operators (mathematics) |
| title | Explicit Bounds for the Pseudospectra of Various Classes of Matrices and Operators |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-21T19%3A16%3A22IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Explicit%20Bounds%20for%20the%20Pseudospectra%20of%20Various%20Classes%20of%20Matrices%20and%20Operators&rft.jtitle=arXiv.org&rft.au=Gong,%20Feixue&rft.date=2015-05-22&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1505.05931&rft_dat=%3Cproquest_arxiv%3E2078951875%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2078951875&rft_id=info:pmid/&rfr_iscdi=true |