{"id":"https://openalex.org/W2019149899","doi":"https://doi.org/10.1137/s0895479894276370","title":"On Two-Sided Bounds Related to Weakly Diagonally Dominant <i>M</i>-Matrices with Application to Digital Circuit Dynamics","display_name":"On Two-Sided Bounds Related to Weakly Diagonally Dominant <i>M</i>-Matrices with Application to Digital Circuit Dynamics","publication_year":1996,"publication_date":"1996-04-01","ids":{"openalex":"https://openalex.org/W2019149899","doi":"https://doi.org/10.1137/s0895479894276370","mag":"2019149899"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479894276370","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479894276370","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078014413","display_name":"P. N. Shivakumar","orcid":"https://orcid.org/0000-0001-9101-9687"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. N. Shivakumar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051760662","display_name":"J. J. Williams","orcid":"https://orcid.org/0000-0003-4715-4501"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joseph J. Williams","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100417960","display_name":"Qiang Ye","orcid":"https://orcid.org/0000-0002-8208-6295"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qiang Ye","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054792311","display_name":"Corneliu A. Marinov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Corneliu A. Marinov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0215,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.75154883,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"17","issue":"2","first_page":"298","last_page":"312"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10363","display_name":"Low-power high-performance VLSI design","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8569687604904175},{"id":"https://openalex.org/keywords/diagonally-dominant-matrix","display_name":"Diagonally dominant matrix","score":0.8531825542449951},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7192232012748718},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5627413988113403},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5508378744125366},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.5221381783485413},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.49560463428497314},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4846985340118408},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44366538524627686},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.42391374707221985},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4219130277633667},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38217341899871826},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3790319859981537},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35303711891174316},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2857099175453186},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.16852647066116333},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10017997026443481}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8569687604904175},{"id":"https://openalex.org/C84507854","wikidata":"https://www.wikidata.org/wiki/Q952222","display_name":"Diagonally dominant matrix","level":3,"score":0.8531825542449951},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7192232012748718},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5627413988113403},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5508378744125366},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.5221381783485413},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.49560463428497314},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4846985340118408},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44366538524627686},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.42391374707221985},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4219130277633667},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38217341899871826},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3790319859981537},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35303711891174316},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2857099175453186},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.16852647066116333},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10017997026443481},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479894276370","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479894276370","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1589334904","https://openalex.org/W1984819558","https://openalex.org/W2035262574","https://openalex.org/W2045099285","https://openalex.org/W2046211369","https://openalex.org/W2054557638","https://openalex.org/W2071491310","https://openalex.org/W2078706244","https://openalex.org/W2163626738","https://openalex.org/W2253469124","https://openalex.org/W2315387399","https://openalex.org/W2328786999","https://openalex.org/W2569133694","https://openalex.org/W4251013638","https://openalex.org/W4302562054"],"related_works":["https://openalex.org/W2136336099","https://openalex.org/W2550293690","https://openalex.org/W1529195008","https://openalex.org/W2031726779","https://openalex.org/W2357224165","https://openalex.org/W2293691459","https://openalex.org/W2139574475","https://openalex.org/W2073772681","https://openalex.org/W2952346244","https://openalex.org/W2106537516"],"abstract_inverted_index":{"Let":[0],"A":[1,93],"be":[2],"a":[3,82,97],"real":[4],"weakly":[5],"diagonally":[6],"dominant":[7],"M-matrix.":[8],"We":[9],"establish":[10],"upper":[11],"and":[12,25,49,89],"lower":[13],"bounds":[14,42],"for":[15,21,26,43,99],"the":[16,27,30,45,50,54,61,100,110],"minimal":[17],"eigenvalue":[18],"of":[19,29,32,53,84,96,103],"A,":[20],"its":[22],"corresponding":[23],"eigenvector,":[24],"entries":[28],"inverse":[31],"A.":[33],"Our":[34],"results":[35],"are":[36],"applied":[37],"to":[38,60,108],"find":[39],"meaningful":[40],"two-sided":[41],"both":[44],"$\\ell":[46],"_1":[47],"$-norm":[48],"weighted":[51],"Perron-norm":[52],"solution":[55],"$x":[56],"(":[57,71],"t":[58],")$":[59],"linear":[62],"differential":[63],"system":[64],"$\\dot":[65],"x":[66,70],"=":[67,74],"-":[68],"Ax,\\,":[69],"0":[72],")":[73],"x_0":[75],">":[76],"0$.":[77],"These":[78],"systems":[79],"occur":[80],"in":[81],"number":[83],"applications,":[85],"including":[86],"compartmental":[87],"analysis":[88,95],"RC":[90],"electrical":[91],"circuits.":[92],"detailed":[94],"model":[98],"transient":[101],"behaviour":[102],"digital":[104],"circuits":[105],"is":[106],"given":[107],"illustrate":[109],"theory.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}