Submatrices with the best-bounded inverses: revisiting the hypothesis
The following hypothesis was put forward by Goreinov, Tyrtyshnikov and Zamarashkin in \cite{GTZ1997}. For arbitrary real \(n \times k\) matrix with orthonormal columns a sufficiently "good" \(k \times k\) submatrix exists. "Good" in the sense of having a bounded spectral norm of...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2024-08 |
|---|---|
| 1. Verfasser: | |
| 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 | Nesterenko, Yuri |
| description | The following hypothesis was put forward by Goreinov, Tyrtyshnikov and Zamarashkin in \cite{GTZ1997}. For arbitrary real \(n \times k\) matrix with orthonormal columns a sufficiently "good" \(k \times k\) submatrix exists. "Good" in the sense of having a bounded spectral norm of its inverse. The hypothesis says that for arbitrary \(k = 1, \ldots, n-1\) the upper bound can be set at \(\sqrt{n}\). Supported by numerical experiments, the problem remained open for all non-trivial cases (\(1 < k < n-1\)). In this paper we will give the proof for the simplest of them (\(n = 4, \, k = 2\)). |
| format | Article |
| fullrecord | <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2787019186</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2787019186</sourcerecordid><originalsourceid>FETCH-proquest_journals_27870191863</originalsourceid><addsrcrecordid>eNqNjNEKgjAUQEcQJOU_DHoW5pa6eg2j93oXzVteqc12N6O_T6IP6Ok8nMOZsUgqlSZ6I-WCxUS9EELmhcwyFbHyFJpH7R1egPgLfcd9B7wB8kljg2mh5WhGcAS04w5GJPRobt-qew92IiGt2Pxa3wniH5dsfSjP-2MyOPsM06zqbXBmUpUsdCHSbapz9V_1Ad1xO8U</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2787019186</pqid></control><display><type>article</type><title>Submatrices with the best-bounded inverses: revisiting the hypothesis</title><source>Free E- Journals</source><creator>Nesterenko, Yuri</creator><creatorcontrib>Nesterenko, Yuri</creatorcontrib><description>The following hypothesis was put forward by Goreinov, Tyrtyshnikov and Zamarashkin in \cite{GTZ1997}. For arbitrary real \(n \times k\) matrix with orthonormal columns a sufficiently "good" \(k \times k\) submatrix exists. "Good" in the sense of having a bounded spectral norm of its inverse. The hypothesis says that for arbitrary \(k = 1, \ldots, n-1\) the upper bound can be set at \(\sqrt{n}\). Supported by numerical experiments, the problem remained open for all non-trivial cases (\(1 < k < n-1\)). In this paper we will give the proof for the simplest of them (\(n = 4, \, k = 2\)).</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Hypotheses ; Upper bounds</subject><ispartof>arXiv.org, 2024-08</ispartof><rights>2024. 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><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>780,784</link.rule.ids></links><search><creatorcontrib>Nesterenko, Yuri</creatorcontrib><title>Submatrices with the best-bounded inverses: revisiting the hypothesis</title><title>arXiv.org</title><description>The following hypothesis was put forward by Goreinov, Tyrtyshnikov and Zamarashkin in \cite{GTZ1997}. For arbitrary real \(n \times k\) matrix with orthonormal columns a sufficiently "good" \(k \times k\) submatrix exists. "Good" in the sense of having a bounded spectral norm of its inverse. The hypothesis says that for arbitrary \(k = 1, \ldots, n-1\) the upper bound can be set at \(\sqrt{n}\). Supported by numerical experiments, the problem remained open for all non-trivial cases (\(1 < k < n-1\)). In this paper we will give the proof for the simplest of them (\(n = 4, \, k = 2\)).</description><subject>Hypotheses</subject><subject>Upper bounds</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNjNEKgjAUQEcQJOU_DHoW5pa6eg2j93oXzVteqc12N6O_T6IP6Ok8nMOZsUgqlSZ6I-WCxUS9EELmhcwyFbHyFJpH7R1egPgLfcd9B7wB8kljg2mh5WhGcAS04w5GJPRobt-qew92IiGt2Pxa3wniH5dsfSjP-2MyOPsM06zqbXBmUpUsdCHSbapz9V_1Ad1xO8U</recordid><startdate>20240826</startdate><enddate>20240826</enddate><creator>Nesterenko, Yuri</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>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20240826</creationdate><title>Submatrices with the best-bounded inverses: revisiting the hypothesis</title><author>Nesterenko, Yuri</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_27870191863</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Hypotheses</topic><topic>Upper bounds</topic><toplevel>online_resources</toplevel><creatorcontrib>Nesterenko, Yuri</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>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nesterenko, Yuri</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Submatrices with the best-bounded inverses: revisiting the hypothesis</atitle><jtitle>arXiv.org</jtitle><date>2024-08-26</date><risdate>2024</risdate><eissn>2331-8422</eissn><abstract>The following hypothesis was put forward by Goreinov, Tyrtyshnikov and Zamarashkin in \cite{GTZ1997}. For arbitrary real \(n \times k\) matrix with orthonormal columns a sufficiently "good" \(k \times k\) submatrix exists. "Good" in the sense of having a bounded spectral norm of its inverse. The hypothesis says that for arbitrary \(k = 1, \ldots, n-1\) the upper bound can be set at \(\sqrt{n}\). Supported by numerical experiments, the problem remained open for all non-trivial cases (\(1 < k < n-1\)). In this paper we will give the proof for the simplest of them (\(n = 4, \, k = 2\)).</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2024-08 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_proquest_journals_2787019186 |
| source | Free E- Journals |
| subjects | Hypotheses Upper bounds |
| title | Submatrices with the best-bounded inverses: revisiting the hypothesis |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-27T00%3A21%3A31IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Submatrices%20with%20the%20best-bounded%20inverses:%20revisiting%20the%20hypothesis&rft.jtitle=arXiv.org&rft.au=Nesterenko,%20Yuri&rft.date=2024-08-26&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2787019186%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2787019186&rft_id=info:pmid/&rfr_iscdi=true |