{"id":"https://openalex.org/W2072858942","doi":"https://doi.org/10.1007/s004930050052","title":"Quick Approximation to Matrices and Applications","display_name":"Quick Approximation to Matrices and Applications","publication_year":1999,"publication_date":"1999-02-01","ids":{"openalex":"https://openalex.org/W2072858942","doi":"https://doi.org/10.1007/s004930050052","mag":"2072858942"},"language":"en","primary_location":{"id":"doi:10.1007/s004930050052","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s004930050052","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","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/A5056950019","display_name":"Alan Frieze","orcid":"https://orcid.org/0000-0002-8481-5615"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]},{"id":"https://openalex.org/I4210124601","display_name":"Department of Mathematical Sciences","ror":"https://ror.org/02xkdev90","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210124601"]}],"countries":["RU","US"],"is_corresponding":true,"raw_author_name":"Alan Frieze","raw_affiliation_strings":["Department of Mathematical Sciences, Carnegie Mellon University; USA;","Department of Mathematical Sciences, Carnegie Mellon University; USA; E-mail: alan@random.math.cmu.edu, , US"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Carnegie Mellon University; USA;","institution_ids":["https://openalex.org/I74973139","https://openalex.org/I4210124601"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Carnegie Mellon University; USA; E-mail: alan@random.math.cmu.edu, , US","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059436381","display_name":"Ravi Kannan","orcid":null},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ravi Kannan","raw_affiliation_strings":["Department of Computer Science, Yale University; USA;","Department of Computer Science, Yale University; USA; E-mail: kannan@cs.yale.edu, , US"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Yale University; USA;","institution_ids":["https://openalex.org/I32971472"]},{"raw_affiliation_string":"Department of Computer Science, Yale University; USA; E-mail: kannan@cs.yale.edu, , US","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056950019"],"corresponding_institution_ids":["https://openalex.org/I4210124601","https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":13.1868,"has_fulltext":false,"cited_by_count":517,"citation_normalized_percentile":{"value":0.9927168,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"19","issue":"2","first_page":"175","last_page":"220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9994000196456909,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9991000294685364,"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":0.7905837297439575},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.7602789402008057},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.683058500289917},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6080148220062256},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5494656562805176},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.49395352602005005},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.463980495929718},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4485465884208679},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.44719645380973816},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.4224262237548828},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.4213690459728241},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1036706268787384},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09237688779830933}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7905837297439575},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7602789402008057},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.683058500289917},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6080148220062256},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5494656562805176},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.49395352602005005},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.463980495929718},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4485465884208679},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.44719645380973816},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.4224262237548828},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.4213690459728241},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1036706268787384},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09237688779830933},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s004930050052","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s004930050052","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.40.2892","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.2892","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cluster.cs.yale.edu/Papers/regularity.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.50.1530","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.1530","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cmu.edu/~af1p/matrix.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.75.7022","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.75.7022","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.yale.edu/users/kannan/Papers/regularity.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1551595104","https://openalex.org/W2004694806","https://openalex.org/W2019363670","https://openalex.org/W2019367452","https://openalex.org/W2027048490","https://openalex.org/W2027105889","https://openalex.org/W2027974205","https://openalex.org/W2038225707","https://openalex.org/W2046097442","https://openalex.org/W2068871408","https://openalex.org/W2083580384","https://openalex.org/W2103012681","https://openalex.org/W2105457218","https://openalex.org/W2106285343","https://openalex.org/W2108932844","https://openalex.org/W2109694798","https://openalex.org/W2116537669","https://openalex.org/W2141072246","https://openalex.org/W2143391442","https://openalex.org/W2145702572","https://openalex.org/W2150420791","https://openalex.org/W2156397150","https://openalex.org/W2156516121"],"related_works":["https://openalex.org/W4224943664","https://openalex.org/W2954167023","https://openalex.org/W2064351239","https://openalex.org/W2949665548","https://openalex.org/W2114983089","https://openalex.org/W1993984283","https://openalex.org/W3186402499","https://openalex.org/W2063422058","https://openalex.org/W2950188642","https://openalex.org/W2109693504"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":25},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":24},{"year":2020,"cited_by_count":28},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":25},{"year":2017,"cited_by_count":25},{"year":2016,"cited_by_count":16},{"year":2015,"cited_by_count":24},{"year":2014,"cited_by_count":29},{"year":2013,"cited_by_count":25},{"year":2012,"cited_by_count":25}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}