{"id":"https://openalex.org/W2030593390","doi":"https://doi.org/10.1145/1577190.1577194","title":"Preconditioning, randomization, solving linear systems, eigen-solving, and root-finding","display_name":"Preconditioning, randomization, solving linear systems, eigen-solving, and root-finding","publication_year":2009,"publication_date":"2009-08-03","ids":{"openalex":"https://openalex.org/W2030593390","doi":"https://doi.org/10.1145/1577190.1577194","mag":"2030593390"},"language":"en","primary_location":{"id":"doi:10.1145/1577190.1577194","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1577190.1577194","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2009 conference on Symbolic numeric computation","raw_type":"proceedings-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/A5056866601","display_name":"Victor Y. Pan","orcid":"https://orcid.org/0000-0002-9819-9358"},"institutions":[{"id":"https://openalex.org/I174216632","display_name":"City University of New York","ror":"https://ror.org/00453a208","country_code":"US","type":"education","lineage":["https://openalex.org/I174216632"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Victor Y. Pan","raw_affiliation_strings":["City University of New York, Bronx, NY, USA","City University of New York, Bronx, NY, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"City University of New York, Bronx, NY, USA","institution_ids":["https://openalex.org/I174216632"]},{"raw_affiliation_string":"City University of New York, Bronx, NY, USA#TAB#","institution_ids":["https://openalex.org/I174216632"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110293006","display_name":"Guoliang Qian","orcid":null},"institutions":[{"id":"https://openalex.org/I174216632","display_name":"City University of New York","ror":"https://ror.org/00453a208","country_code":"US","type":"education","lineage":["https://openalex.org/I174216632"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guoliang Qian","raw_affiliation_strings":["City University of New York, New York, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"City University of New York, New York, NY, USA","institution_ids":["https://openalex.org/I174216632"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007207817","display_name":"Ai-Long Zheng","orcid":null},"institutions":[{"id":"https://openalex.org/I174216632","display_name":"City University of New York","ror":"https://ror.org/00453a208","country_code":"US","type":"education","lineage":["https://openalex.org/I174216632"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ai-Long Zheng","raw_affiliation_strings":["City University of New York, New York, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"City University of New York, New York, NY, USA","institution_ids":["https://openalex.org/I174216632"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I174216632"],"apc_list":null,"apc_paid":null,"fwci":0.3546,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.61247361,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"5","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9980000257492065,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9975000023841858,"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/root","display_name":"Root (linguistics)","score":0.6605958938598633},{"id":"https://openalex.org/keywords/preprocessor","display_name":"Preprocessor","score":0.6172420382499695},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.5693408250808716},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5574048757553101},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5266119241714478},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5049620270729065},{"id":"https://openalex.org/keywords/randomization","display_name":"Randomization","score":0.4912065863609314},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.4796876609325409},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47627848386764526},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4512249529361725},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44426220655441284},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3662498891353607},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36283713579177856},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12276527285575867},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1100248396396637},{"id":"https://openalex.org/keywords/randomized-controlled-trial","display_name":"Randomized controlled trial","score":0.09134432673454285}],"concepts":[{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.6605958938598633},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.6172420382499695},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.5693408250808716},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5574048757553101},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5266119241714478},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5049620270729065},{"id":"https://openalex.org/C204243189","wikidata":"https://www.wikidata.org/wiki/Q1363085","display_name":"Randomization","level":3,"score":0.4912065863609314},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.4796876609325409},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47627848386764526},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4512249529361725},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44426220655441284},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3662498891353607},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36283713579177856},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12276527285575867},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1100248396396637},{"id":"https://openalex.org/C168563851","wikidata":"https://www.wikidata.org/wiki/Q1436668","display_name":"Randomized controlled trial","level":2,"score":0.09134432673454285},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C141071460","wikidata":"https://www.wikidata.org/wiki/Q40821","display_name":"Surgery","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1577190.1577194","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1577190.1577194","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2009 conference on Symbolic numeric computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W21639112","https://openalex.org/W1489355995","https://openalex.org/W1502124338","https://openalex.org/W1560263223","https://openalex.org/W1968245619","https://openalex.org/W1976998625","https://openalex.org/W1995134626","https://openalex.org/W2049417271","https://openalex.org/W2059067170","https://openalex.org/W2113361400","https://openalex.org/W2144619406","https://openalex.org/W2798909945","https://openalex.org/W4205624883"],"related_works":["https://openalex.org/W195825275","https://openalex.org/W153415882","https://openalex.org/W2365527693","https://openalex.org/W2739650862","https://openalex.org/W4252024106","https://openalex.org/W3097421206","https://openalex.org/W2500993308","https://openalex.org/W2035371040","https://openalex.org/W2389121573","https://openalex.org/W4386576538"],"abstract_inverted_index":{"We":[0],"propose":[1],"novel":[2],"randomized":[3],"preprocessing":[4],"techniques":[5],"for":[6],"solving":[7],"linear":[8],"systems":[9],"of":[10,19,43],"equations":[11],"and":[12,21,29],"eigen-solving":[13],"with":[14],"extensions":[15],"to":[16,25,36],"the":[17,32,41],"solution":[18],"polynomial":[20],"secular":[22],"equations.":[23],"According":[24],"our":[26],"formal":[27],"study":[28],"extensive":[30],"experiments,":[31],"approach":[33],"turns":[34],"out":[35],"be":[37],"effective,":[38],"particularly":[39],"in":[40],"case":[42],"structured":[44],"input":[45],"matrices.":[46]},"counts_by_year":[],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}