{"id":"https://openalex.org/W3033776753","doi":"https://doi.org/10.1017/s1446181120000061","title":"STREAMLINED SOLUTIONS TO MULTILEVEL SPARSE MATRIX PROBLEMS","display_name":"STREAMLINED SOLUTIONS TO MULTILEVEL SPARSE MATRIX PROBLEMS","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3033776753","doi":"https://doi.org/10.1017/s1446181120000061","mag":"3033776753"},"language":"en","primary_location":{"id":"doi:10.1017/s1446181120000061","doi":"https://doi.org/10.1017/s1446181120000061","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s1446181120000061","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/606582E7E1A4E0A60DAD9971B7EA3874/S1446181120000061a.pdf/div-class-title-streamlined-solutions-to-multilevel-sparse-matrix-problems-div.pdf","source":{"id":"https://openalex.org/S109939064","display_name":"The ANZIAM Journal","issn_l":"1446-1811","issn":["1446-1811","1446-8735"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The ANZIAM Journal","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/606582E7E1A4E0A60DAD9971B7EA3874/S1446181120000061a.pdf/div-class-title-streamlined-solutions-to-multilevel-sparse-matrix-problems-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073881810","display_name":"Tui H. Nolan","orcid":"https://orcid.org/0000-0003-1877-7857","observed_orcids":["https://orcid.org/0000-0003-1877-7857"]},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"TUI H. NOLAN","raw_affiliation_strings":["University of Technology Sydney, P.O. Box 123, Broadway, New South Wales2007, Australia email","University of Technology Sydney"],"raw_orcid":"https://orcid.org/0000-0003-1877-7857","affiliations":[{"raw_affiliation_string":"University of Technology Sydney, P.O. Box 123, Broadway, New South Wales2007, Australia email","institution_ids":["https://openalex.org/I114017466"]},{"raw_affiliation_string":"University of Technology Sydney","institution_ids":["https://openalex.org/I114017466"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050191159","display_name":"MATTHEW P. WAND","orcid":"https://orcid.org/0000-0003-2555-896X","observed_orcids":["https://orcid.org/0000-0003-2555-896X"]},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"MATT P. WAND","raw_affiliation_strings":["University of Technology Sydney, P.O. Box 123, Broadway, New South Wales2007, Australia email","University of Technology Sydney"],"raw_orcid":"https://orcid.org/0000-0003-2555-896X","affiliations":[{"raw_affiliation_string":"University of Technology Sydney, P.O. Box 123, Broadway, New South Wales2007, Australia email","institution_ids":["https://openalex.org/I114017466"]},{"raw_affiliation_string":"University of Technology Sydney","institution_ids":["https://openalex.org/I114017466"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050191159"],"corresponding_institution_ids":["https://openalex.org/I114017466"],"apc_list":{"value":1500,"currency":"USD","value_usd":1500},"apc_paid":null,"fwci":0.7209,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71924166,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"62","issue":"1","first_page":"18","last_page":"41"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.8246999979019165,"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":0.8246999979019165,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.09969999641180038,"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/T11911","display_name":"Spatial and Panel Data Analysis","score":0.013700000010430813,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multilevel-modelling","display_name":"multilevel modelling","score":0.890999972820282},{"id":"https://openalex.org/keywords/nested-random-effects","display_name":"nested random effects","score":0.6710000038146973},{"id":"https://openalex.org/keywords/matrix-inversion","display_name":"matrix inversion","score":0.45399999618530273},{"id":"https://openalex.org/keywords/linear-systems","display_name":"linear systems","score":0.7490000128746033},{"id":"https://openalex.org/keywords/standard-errors","display_name":"standard errors","score":0.6700000166893005},{"id":"https://openalex.org/keywords/hierarchical-models","display_name":"hierarchical models","score":0.3610000014305115}],"concepts":[{"id":"https://openalex.org/C162376815","wikidata":"https://www.wikidata.org/wiki/Q2158281","display_name":"Frequentist inference","level":4,"score":0.8264065980911255},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5964944362640381},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5200443267822266},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.501396656036377},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.4555675685405731},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.44731906056404114},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44039663672447205},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.43646275997161865},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41093704104423523},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4075102210044861},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37990081310272217},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3419203758239746},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19619932770729065},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.1707431972026825},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07271996140480042},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1017/s1446181120000061","doi":"https://doi.org/10.1017/s1446181120000061","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s1446181120000061","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/606582E7E1A4E0A60DAD9971B7EA3874/S1446181120000061a.pdf/div-class-title-streamlined-solutions-to-multilevel-sparse-matrix-problems-div.pdf","source":{"id":"https://openalex.org/S109939064","display_name":"The ANZIAM Journal","issn_l":"1446-1811","issn":["1446-1811","1446-8735"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The ANZIAM Journal","raw_type":"journal-article"},{"id":"doi:10.21914/anziamj.v62i0.14621","doi":"https://doi.org/10.21914/anziamj.v62i0.14621","is_oa":false,"landing_page_url":"https://doi.org/10.21914/anziamj.v62i0.14621","pdf_url":null,"source":{"id":"https://openalex.org/S4210233119","display_name":"ANZIAM Journal","issn_l":"0334-2700","issn":["0334-2700","1445-8810","1839-4078"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ANZIAM Journal","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1903.03089","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.03089","pdf_url":"https://arxiv.org/pdf/1903.03089","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:opus.lib.uts.edu.au:10453/146961","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10453/146961","pdf_url":"https://opus.lib.uts.edu.au/bitstream/10453/146961/2/Nolan20preprint.pdf","source":{"id":"https://openalex.org/S4377196279","display_name":"OPUS - Open Publications of UTS Scholars (University of Technology Sydney)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I114017466","host_organization_name":"University of Technology Sydney","host_organization_lineage":["https://openalex.org/I114017466"],"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":null,"raw_type":"Journal Article"},{"id":"mag:2921253951","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1903.03089v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1903.03089","doi":"https://doi.org/10.48550/arxiv.1903.03089","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1903.03089","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1017/s1446181120000061","doi":"https://doi.org/10.1017/s1446181120000061","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s1446181120000061","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/606582E7E1A4E0A60DAD9971B7EA3874/S1446181120000061a.pdf/div-class-title-streamlined-solutions-to-multilevel-sparse-matrix-problems-div.pdf","source":{"id":"https://openalex.org/S109939064","display_name":"The ANZIAM Journal","issn_l":"1446-1811","issn":["1446-1811","1446-8735"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The ANZIAM Journal","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3270893917","display_name":"Semiparametric Regression for Streaming Data","funder_award_id":"DP140100441","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3033776753.pdf","grobid_xml":"https://content.openalex.org/works/W3033776753.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1484712862","https://openalex.org/W1495656322","https://openalex.org/W1531439921","https://openalex.org/W1565240145","https://openalex.org/W1587094587","https://openalex.org/W1963669198","https://openalex.org/W2005991795","https://openalex.org/W2011981966","https://openalex.org/W2030769837","https://openalex.org/W2056156011","https://openalex.org/W2101950184","https://openalex.org/W2269254960","https://openalex.org/W2500845915","https://openalex.org/W2570625295","https://openalex.org/W2797925981","https://openalex.org/W2894500951","https://openalex.org/W2921735706","https://openalex.org/W2949924781","https://openalex.org/W4206103160","https://openalex.org/W4206439534","https://openalex.org/W4288418830","https://openalex.org/W4293258550","https://openalex.org/W4300157606","https://openalex.org/W4300579247"],"related_works":["https://openalex.org/W2999723002","https://openalex.org/W2921253951","https://openalex.org/W4413493162","https://openalex.org/W2086517348","https://openalex.org/W4396508364","https://openalex.org/W3006706427","https://openalex.org/W4288418830","https://openalex.org/W1978190826","https://openalex.org/W3096492763","https://openalex.org/W2039954784"],"abstract_inverted_index":{"We":[0,47],"define":[1],"and":[2,14,53,56,92],"solve":[3],"classes":[4,18],"of":[5,24,70,82,96],"sparse":[6],"matrix":[7,86],"problems":[8,29],"that":[9],"arise":[10],"in":[11,35,66,99],"multilevel":[12],"modelling":[13],"data":[15,37],"analysis.":[16],"The":[17],"are":[19,41,78,90],"indexed":[20],"by":[21],"the":[22,32,62,71],"number":[23],"nested":[25],"units,":[26],"with":[27],"two-level":[28,45,52],"corresponding":[30],"to":[31],"common":[33],"situation,":[34],"which":[36],"on":[38],"level-1":[39],"units":[40],"grouped":[42],"within":[43],"a":[44,79],"structure.":[46],"provide":[48,59],"full":[49],"solutions":[50,77],"for":[51,61,112],"three-level":[54],"problems,":[55],"their":[57],"derivations":[58],"blueprints":[60],"challenging,":[63],"albeit":[64],"rarer":[65],"applications,":[67],"higher-level":[68,115],"versions":[69],"problem.":[72],"While":[73],"our":[74,85],"linear":[75],"system":[76],"concise":[80],"recasting":[81],"existing":[83],"results,":[84],"inverse":[87],"sub-block":[88],"results":[89],"novel":[91],"facilitate":[93],"streamlined":[94,106],"computation":[95],"standard":[97],"errors":[98],"frequentist":[100],"inference":[101,111],"as":[102,104],"well":[103],"allowing":[105],"mean":[107],"field":[108],"variational":[109],"Bayesian":[110],"models":[113],"containing":[114],"random":[116],"effects.":[117],"doi:":[118],"10.1017/S1446181120000061":[119]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2020-06-12T00:00:00"}
