{"id":"https://openalex.org/W2052169089","doi":"https://doi.org/10.1137/080729463","title":"Componentwise Condition Numbers of Random Sparse Matrices","display_name":"Componentwise Condition Numbers of Random Sparse Matrices","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2052169089","doi":"https://doi.org/10.1137/080729463","mag":"2052169089"},"language":"en","primary_location":{"id":"doi:10.1137/080729463","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080729463","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":true,"oa_status":"bronze","oa_url":"https://scholars.cityu.edu.hk/en/publications/componentwise-condition-numbers-of-random-sparse-matrices","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036450487","display_name":"Dennis Cheung","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dennis Cheung","raw_affiliation_strings":["dennisc@uic.edu.hk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"dennisc@uic.edu.hk#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079608792","display_name":"Felipe Cucker","orcid":"https://orcid.org/0000-0002-4569-3248"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Felipe Cucker","raw_affiliation_strings":["macucker@cityu.edu.hk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"macucker@cityu.edu.hk#TAB#","institution_ids":[]}]}],"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":4,"citation_normalized_percentile":{"value":0.11800303,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"31","issue":"2","first_page":"721","last_page":"731"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.975600004196167,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9695000052452087,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.8644428253173828},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49595603346824646},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46314120292663574},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.44136473536491394},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35636353492736816},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26965904235839844}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8644428253173828},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49595603346824646},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46314120292663574},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.44136473536491394},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35636353492736816},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26965904235839844},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/080729463","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080729463","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"},{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/componentwise-condition-numbers-of-random-sparse-matrices","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"},{"id":"pmh:oai:pure.atira.dk:publications/4fef9a0e-7a67-46ae-8b4a-724efc5af557","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/4fef9a0e-7a67-46ae-8b4a-724efc5af557","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cheung, D & Cucker, F 2009, 'Componentwise condition numbers of random sparse matrices', SIAM Journal on Matrix Analysis and Applications, vol. 31, no. 2, pp. 721-731. https://doi.org/10.1137/080729463","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/componentwise-condition-numbers-of-random-sparse-matrices","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1966287322","https://openalex.org/W1975348634","https://openalex.org/W1976125652","https://openalex.org/W2010072984","https://openalex.org/W2030638350","https://openalex.org/W2078488968","https://openalex.org/W2079400692","https://openalex.org/W2115780241","https://openalex.org/W2125212434"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2017331178","https://openalex.org/W2964072617","https://openalex.org/W2976797620","https://openalex.org/W2260035625","https://openalex.org/W2090649758","https://openalex.org/W2331592954","https://openalex.org/W2045490848","https://openalex.org/W1987949650","https://openalex.org/W4249089511"],"abstract_inverted_index":{"We":[0],"prove":[1],"an":[2],"${\\cal":[3],"O}(\\log":[4],"n)$":[5],"bound":[6],"for":[7,42],"the":[8,12,15,20,37],"expected":[9],"value":[10],"of":[11,14,24,40],"logarithm":[13],"componentwise":[16],"(and,":[17],"a":[18,25,32],"fortiori,":[19],"mixed)":[21],"condition":[22],"number":[23],"random":[26],"sparse":[27],"$n\\times":[28],"n$":[29],"matrix.":[30],"As":[31],"consequence,":[33],"small":[34],"bounds":[35],"on":[36],"average":[38],"loss":[39],"accuracy":[41],"triangular":[43],"linear":[44],"systems":[45],"follow.":[46]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-25T09:21:30.201066","created_date":"2025-10-10T00:00:00"}
