{"id":"https://openalex.org/W4386539915","doi":"https://doi.org/10.1137/22m1538648","title":"Randomized Low-Rank Approximation for Symmetric Indefinite Matrices","display_name":"Randomized Low-Rank Approximation for Symmetric Indefinite Matrices","publication_year":2023,"publication_date":"2023-09-08","ids":{"openalex":"https://openalex.org/W4386539915","doi":"https://doi.org/10.1137/22m1538648"},"language":"en","primary_location":{"id":"doi:10.1137/22m1538648","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1538648","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/A5008129578","display_name":"Yuji Nakatsukasa","orcid":"https://orcid.org/0000-0001-7911-1501"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Yuji Nakatsukasa","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK","Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK,"],"raw_orcid":"https://orcid.org/0000-0001-7911-1501","affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK,","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020203272","display_name":"Taejun Park","orcid":"https://orcid.org/0000-0001-8759-6705"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Taejun Park","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK","Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK,"],"raw_orcid":"https://orcid.org/0000-0001-8759-6705","affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK,","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020203272"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":1.6466,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.85261737,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"44","issue":"3","first_page":"1370","last_page":"1392"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9995999932289124,"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":0.9995999932289124,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9976000189781189,"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":0.8591755628585815},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.695712685585022},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.6869078874588013},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.653304934501648},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5993140935897827},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.533397912979126},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5268843770027161},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5196129679679871},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.47324830293655396},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4470606744289398},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.43701618909835815},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4206402897834778},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38938167691230774},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2643420696258545},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.10737329721450806}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8591755628585815},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.695712685585022},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.6869078874588013},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.653304934501648},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5993140935897827},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.533397912979126},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5268843770027161},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5196129679679871},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.47324830293655396},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4470606744289398},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.43701618909835815},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4206402897834778},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38938167691230774},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2643420696258545},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.10737329721450806},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"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},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1538648","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1538648","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1577111082","https://openalex.org/W2013176880","https://openalex.org/W2033244207","https://openalex.org/W2082624758","https://openalex.org/W2117756735","https://openalex.org/W2120157859","https://openalex.org/W2141696759","https://openalex.org/W2171810522","https://openalex.org/W2492794003","https://openalex.org/W2569261326","https://openalex.org/W2580753685","https://openalex.org/W2772646190","https://openalex.org/W2805127664","https://openalex.org/W2963455674","https://openalex.org/W2964361301","https://openalex.org/W3100283647","https://openalex.org/W3102506524","https://openalex.org/W3108353645","https://openalex.org/W3112410551","https://openalex.org/W4213311204","https://openalex.org/W4229706427","https://openalex.org/W4283657107"],"related_works":["https://openalex.org/W4366831400","https://openalex.org/W2158044763","https://openalex.org/W2168915192","https://openalex.org/W4221157149","https://openalex.org/W4298234822","https://openalex.org/W2782047334","https://openalex.org/W1970576574","https://openalex.org/W3017414697","https://openalex.org/W2522507432","https://openalex.org/W605362495"],"abstract_inverted_index":{"The":[0,18,84],"Nystr\u00f6m":[1,48],"method":[2,19],"is":[3,94],"a":[4,9,13,47,60,89],"popular":[5],"choice":[6],"for":[7,28],"finding":[8,46],"low-rank":[10],"approximation":[11,49,75],"to":[12,24,50,88],"symmetric":[14,25,51],"positive":[15],"semidefinite":[16],"matrix.":[17],"can":[20,32],"fail":[21],"when":[22,78],"applied":[23],"indefinite":[26,52],"matrices":[27],"which":[29],"the":[30,42,57,64,73,79],"error":[31],"be":[33],"unboundedly":[34],"large.":[35],"In":[36],"this":[37],"work,":[38],"we":[39],"first":[40],"identify":[41],"main":[43],"challenges":[44],"in":[45],"matrices.":[53],"We":[54],"then":[55],"prove":[56],"existence":[58],"of":[59,72],"variant":[61],"that":[62,76],"overcomes":[63],"instability,":[65],"and":[66],"establish":[67],"relative-error":[68],"nuclear":[69],"norm":[70],"bounds":[71],"resulting":[74],"hold":[77],"singular":[80],"values":[81],"decay":[82],"rapidly.":[83],"analysis":[85],"naturally":[86],"leads":[87],"practical":[90],"algorithm,":[91],"whose":[92],"robustness":[93],"illustrated":[95],"with":[96],"experiments.":[97]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2023-09-09T00:00:00"}
