Block diagonal dominance of matrices revisited: Bounds for the norms of inverses and eigenvalue inclusion sets

We generalize the bounds on the inverses of diagonally dominant matrices obtained in [16] from scalar to block tridiagonal matrices. Our derivations are based on a generalization of the classical condition of block diagonal dominance of matrices given by Feingold and Varga in [11]. Based on this gen...

Full description

Saved in:
Bibliographic Details
Published in:Linear algebra and its applications 2018-09, Vol.553, p.365-383
Main Authors: Echeverría, Carlos, Liesen, Jörg, Nabben, Reinhard
Format: Article
Language:English
Subjects:
Block diagonal dominance
Block matrices
Block tridiagonal matrices
Decay bounds for the inverse
Eigenvalue inclusion regions
Eigenvalues
Gershgorin Circle Theorem
Linear algebra
Norms
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c368t-1b0f48b862a6e4bca8b4083560aea5fd6062216df0326189c90ef136590840ba3
cites cdi_FETCH-LOGICAL-c368t-1b0f48b862a6e4bca8b4083560aea5fd6062216df0326189c90ef136590840ba3
container_end_page 383
container_issue
container_start_page 365
container_title Linear algebra and its applications
container_volume 553
creator Echeverría, Carlos
Liesen, Jörg
Nabben, Reinhard
description We generalize the bounds on the inverses of diagonally dominant matrices obtained in [16] from scalar to block tridiagonal matrices. Our derivations are based on a generalization of the classical condition of block diagonal dominance of matrices given by Feingold and Varga in [11]. Based on this generalization, which was recently presented in [3], we also derive a variant of the Gershgorin Circle Theorem for general block matrices which can provide tighter spectral inclusion regions than those obtained by Feingold and Varga.
doi_str_mv 10.1016/j.laa.2018.04.025
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2426550836</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0024379518302192</els_id><sourcerecordid>2426550836</sourcerecordid><originalsourceid>FETCH-LOGICAL-c368t-1b0f48b862a6e4bca8b4083560aea5fd6062216df0326189c90ef136590840ba3</originalsourceid><addsrcrecordid>eNp9kE1LAzEQhoMoWD9-gLeA510n2Wya6knFLxC86Dlkk9mauk1qslvw35tSz54Ghud9mXkIuWBQM2DyalUPxtQcmKpB1MDbAzJjat5UTLXykMwAuKia-aI9Jic5rwBAzIHPSLgbov2izptlDGagLq59MMEijT1dmzF5i5km3PrsR3TX9C5OwWXax0THT6QhpnXesT5sMeXCmuAo-iWGrRkmLHs7TNnHQDOO-Ywc9WbIeP43T8nH48P7_XP1-vb0cn_7WtlGqrFiHfRCdUpyI1F01qhOgGpaCQZN2zsJknMmXQ8Nl0wt7AKwZ41sF6AEdKY5JZf73k2K3xPmUa_ilMqDWXPBZduWNlkotqdsijkn7PUm-bVJP5qB3mnVK1206p1WDUIXrSVzs89gOX_rMelsPRZhzie0o3bR_5P-Ba9ngHM</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2426550836</pqid></control><display><type>article</type><title>Block diagonal dominance of matrices revisited: Bounds for the norms of inverses and eigenvalue inclusion sets</title><source>ScienceDirect Journals</source><creator>Echeverría, Carlos ; Liesen, Jörg ; Nabben, Reinhard</creator><creatorcontrib>Echeverría, Carlos ; Liesen, Jörg ; Nabben, Reinhard</creatorcontrib><description>We generalize the bounds on the inverses of diagonally dominant matrices obtained in [16] from scalar to block tridiagonal matrices. Our derivations are based on a generalization of the classical condition of block diagonal dominance of matrices given by Feingold and Varga in [11]. Based on this generalization, which was recently presented in [3], we also derive a variant of the Gershgorin Circle Theorem for general block matrices which can provide tighter spectral inclusion regions than those obtained by Feingold and Varga.</description><identifier>ISSN: 0024-3795</identifier><identifier>EISSN: 1873-1856</identifier><identifier>DOI: 10.1016/j.laa.2018.04.025</identifier><language>eng</language><publisher>Amsterdam: Elsevier Inc</publisher><subject>Block diagonal dominance ; Block matrices ; Block tridiagonal matrices ; Decay bounds for the inverse ; Eigenvalue inclusion regions ; Eigenvalues ; Gershgorin Circle Theorem ; Linear algebra ; Norms</subject><ispartof>Linear algebra and its applications, 2018-09, Vol.553, p.365-383</ispartof><rights>2018 Elsevier Inc.</rights><rights>Copyright American Elsevier Company, Inc. Sep 15, 2018</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c368t-1b0f48b862a6e4bca8b4083560aea5fd6062216df0326189c90ef136590840ba3</citedby><cites>FETCH-LOGICAL-c368t-1b0f48b862a6e4bca8b4083560aea5fd6062216df0326189c90ef136590840ba3</cites><orcidid>0000-0002-1670-1405</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Echeverría, Carlos</creatorcontrib><creatorcontrib>Liesen, Jörg</creatorcontrib><creatorcontrib>Nabben, Reinhard</creatorcontrib><title>Block diagonal dominance of matrices revisited: Bounds for the norms of inverses and eigenvalue inclusion sets</title><title>Linear algebra and its applications</title><description>We generalize the bounds on the inverses of diagonally dominant matrices obtained in [16] from scalar to block tridiagonal matrices. Our derivations are based on a generalization of the classical condition of block diagonal dominance of matrices given by Feingold and Varga in [11]. Based on this generalization, which was recently presented in [3], we also derive a variant of the Gershgorin Circle Theorem for general block matrices which can provide tighter spectral inclusion regions than those obtained by Feingold and Varga.</description><subject>Block diagonal dominance</subject><subject>Block matrices</subject><subject>Block tridiagonal matrices</subject><subject>Decay bounds for the inverse</subject><subject>Eigenvalue inclusion regions</subject><subject>Eigenvalues</subject><subject>Gershgorin Circle Theorem</subject><subject>Linear algebra</subject><subject>Norms</subject><issn>0024-3795</issn><issn>1873-1856</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWD9-gLeA510n2Wya6knFLxC86Dlkk9mauk1qslvw35tSz54Ghud9mXkIuWBQM2DyalUPxtQcmKpB1MDbAzJjat5UTLXykMwAuKia-aI9Jic5rwBAzIHPSLgbov2izptlDGagLq59MMEijT1dmzF5i5km3PrsR3TX9C5OwWXax0THT6QhpnXesT5sMeXCmuAo-iWGrRkmLHs7TNnHQDOO-Ywc9WbIeP43T8nH48P7_XP1-vb0cn_7WtlGqrFiHfRCdUpyI1F01qhOgGpaCQZN2zsJknMmXQ8Nl0wt7AKwZ41sF6AEdKY5JZf73k2K3xPmUa_ilMqDWXPBZduWNlkotqdsijkn7PUm-bVJP5qB3mnVK1206p1WDUIXrSVzs89gOX_rMelsPRZhzie0o3bR_5P-Ba9ngHM</recordid><startdate>20180915</startdate><enddate>20180915</enddate><creator>Echeverría, Carlos</creator><creator>Liesen, Jörg</creator><creator>Nabben, Reinhard</creator><general>Elsevier Inc</general><general>American Elsevier Company, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-1670-1405</orcidid></search><sort><creationdate>20180915</creationdate><title>Block diagonal dominance of matrices revisited: Bounds for the norms of inverses and eigenvalue inclusion sets</title><author>Echeverría, Carlos ; Liesen, Jörg ; Nabben, Reinhard</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c368t-1b0f48b862a6e4bca8b4083560aea5fd6062216df0326189c90ef136590840ba3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Block diagonal dominance</topic><topic>Block matrices</topic><topic>Block tridiagonal matrices</topic><topic>Decay bounds for the inverse</topic><topic>Eigenvalue inclusion regions</topic><topic>Eigenvalues</topic><topic>Gershgorin Circle Theorem</topic><topic>Linear algebra</topic><topic>Norms</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Echeverría, Carlos</creatorcontrib><creatorcontrib>Liesen, Jörg</creatorcontrib><creatorcontrib>Nabben, Reinhard</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</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>Linear algebra and its applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Echeverría, Carlos</au><au>Liesen, Jörg</au><au>Nabben, Reinhard</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Block diagonal dominance of matrices revisited: Bounds for the norms of inverses and eigenvalue inclusion sets</atitle><jtitle>Linear algebra and its applications</jtitle><date>2018-09-15</date><risdate>2018</risdate><volume>553</volume><spage>365</spage><epage>383</epage><pages>365-383</pages><issn>0024-3795</issn><eissn>1873-1856</eissn><abstract>We generalize the bounds on the inverses of diagonally dominant matrices obtained in [16] from scalar to block tridiagonal matrices. Our derivations are based on a generalization of the classical condition of block diagonal dominance of matrices given by Feingold and Varga in [11]. Based on this generalization, which was recently presented in [3], we also derive a variant of the Gershgorin Circle Theorem for general block matrices which can provide tighter spectral inclusion regions than those obtained by Feingold and Varga.</abstract><cop>Amsterdam</cop><pub>Elsevier Inc</pub><doi>10.1016/j.laa.2018.04.025</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0002-1670-1405</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0024-3795
ispartof Linear algebra and its applications, 2018-09, Vol.553, p.365-383
issn 0024-3795
1873-1856
language eng
recordid cdi_proquest_journals_2426550836
source ScienceDirect Journals
subjects Block diagonal dominance
Block matrices
Block tridiagonal matrices
Decay bounds for the inverse
Eigenvalue inclusion regions
Eigenvalues
Gershgorin Circle Theorem
Linear algebra
Norms
title Block diagonal dominance of matrices revisited: Bounds for the norms of inverses and eigenvalue inclusion sets
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-04T16%3A07%3A59IST&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=Block%20diagonal%20dominance%20of%20matrices%20revisited:%20Bounds%20for%20the%20norms%20of%20inverses%20and%20eigenvalue%20inclusion%20sets&rft.jtitle=Linear%20algebra%20and%20its%20applications&rft.au=Echeverr%C3%ADa,%20Carlos&rft.date=2018-09-15&rft.volume=553&rft.spage=365&rft.epage=383&rft.pages=365-383&rft.issn=0024-3795&rft.eissn=1873-1856&rft_id=info:doi/10.1016/j.laa.2018.04.025&rft_dat=%3Cproquest_cross%3E2426550836%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c368t-1b0f48b862a6e4bca8b4083560aea5fd6062216df0326189c90ef136590840ba3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2426550836&rft_id=info:pmid/&rfr_iscdi=true