{"id":"https://openalex.org/W1997055142","doi":"https://doi.org/10.1137/0614068","title":"Length Bounds for Singular Values of Sparse Matrices","display_name":"Length Bounds for Singular Values of Sparse Matrices","publication_year":1993,"publication_date":"1993-10-01","ids":{"openalex":"https://openalex.org/W1997055142","doi":"https://doi.org/10.1137/0614068","mag":"1997055142"},"language":"en","primary_location":{"id":"doi:10.1137/0614068","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0614068","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/A5111066366","display_name":"Charles R. Johnson","orcid":"https://orcid.org/0000-0001-8707-8596"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Charles R. Johnson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5026478936","display_name":"Peter Nylen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peter M. Nylen","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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12429058,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"4","first_page":"1043","last_page":"1047"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"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":0.9991999864578247,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9943000078201294,"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/T11476","display_name":"Graph theory and applications","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8978774547576904},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.6836614608764648},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6698291897773743},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.5666514039039612},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4664890766143799},{"id":"https://openalex.org/keywords/complex-matrix","display_name":"Complex matrix","score":0.4306027889251709},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.41673779487609863},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.18884479999542236},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07465499639511108},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.04866665601730347}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8978774547576904},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.6836614608764648},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6698291897773743},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.5666514039039612},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4664890766143799},{"id":"https://openalex.org/C2988629283","wikidata":"https://www.wikidata.org/wiki/Q44337","display_name":"Complex matrix","level":2,"score":0.4306027889251709},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.41673779487609863},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.18884479999542236},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07465499639511108},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.04866665601730347},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0614068","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0614068","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":0,"referenced_works":[],"related_works":["https://openalex.org/W2080672562","https://openalex.org/W2359395995","https://openalex.org/W2014230080","https://openalex.org/W3013272832","https://openalex.org/W2013769791","https://openalex.org/W2268914470","https://openalex.org/W2073728252","https://openalex.org/W4287823279","https://openalex.org/W2736155834","https://openalex.org/W1977512140"],"abstract_inverted_index":{"For":[0],"an":[1],"m-by-n":[2],"matrix":[3],"A":[4,27],"with":[5],"singular":[6],"values":[7],"$\\sigma":[8,71,93],"_1":[9,47,84,94],"\\geqq":[10,13,15,48,51,53],"\\sigma":[11,16],"_2":[12,50],"\\cdots":[14,52],"_n":[17,55],"$,":[18,85],"the":[19,32,37,43,61,90],"following":[20],"is":[21],"observed.":[22],"Concatenate":[23],"all":[24],"rows":[25],"of":[26,42,60],"having":[28],"nonzero":[29],"entries":[30],"in":[31],"ith":[33],"column":[34],"and":[35],"calculate":[36],"Euclidean":[38],"length":[39],"$\\ell_i":[40],"$":[41,56,95],"result.":[44],"Let":[45],"$\\hat{\\ell}":[46,83],"\\hat{\\ell}":[49,54],"be":[57,87],"a":[58],"rearrangement":[59],"numbers":[62],"$\\ell":[63],"_i":[64,72],",\\,i":[65,75],"=":[66,76],"1,":[67,77],"\\ldots":[68,78],",n$.":[69,79],"Then":[70],"\\leqq":[73],"\\hat{\\ell}_i":[74],"Examples":[80],"show":[81],"that":[82],"can":[86],"smaller":[88],"than":[89],"bound":[91],"for":[92],",":[96],"obtained":[97],"by":[98],"applying":[99],"Gersgorin\u2019s":[100],"theorem":[101],"to":[102],"$A^":[103],"*":[104],"A$":[105],".":[106]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
