{"id":"https://openalex.org/W2964203357","doi":"https://doi.org/10.1137/17m1117744","title":"Hierarchical Orthogonal Matrix Generation and Matrix-Vector Multiplications in Rigid Body Simulations","display_name":"Hierarchical Orthogonal Matrix Generation and Matrix-Vector Multiplications in Rigid Body Simulations","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2964203357","doi":"https://doi.org/10.1137/17m1117744","mag":"2964203357","pmid":"https://pubmed.ncbi.nlm.nih.gov/31452593"},"language":"en","primary_location":{"id":"doi:10.1137/17m1117744","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1117744","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6709857","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008332631","display_name":"Fuhui Fang","orcid":null},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]},{"id":"https://openalex.org/I1344073410","display_name":"Howard Hughes Medical Institute","ror":"https://ror.org/006w34k90","country_code":"US","type":"facility","lineage":["https://openalex.org/I1344073410"]},{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]},{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fuhui Fang","raw_affiliation_strings":["Center for Research in Extreme Scale Technologies, Indiana University, Bloomington, IN 47404","Department of Chemistry and Biochemistry and Department of Pharmacology, University of California at San Diego, La Jolla, CA 92093-0365","Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250","Howard Hughes Medical Institute, University of California at San Diego, La Jolla, CA 92093-0365"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Research in Extreme Scale Technologies, Indiana University, Bloomington, IN 47404","institution_ids":["https://openalex.org/I4210119109"]},{"raw_affiliation_string":"Department of Chemistry and Biochemistry and Department of Pharmacology, University of California at San Diego, La Jolla, CA 92093-0365","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250","institution_ids":["https://openalex.org/I114027177"]},{"raw_affiliation_string":"Howard Hughes Medical Institute, University of California at San Diego, La Jolla, CA 92093-0365","institution_ids":["https://openalex.org/I1344073410"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103071826","display_name":"Jingfang Huang","orcid":"https://orcid.org/0000-0002-6720-8389"},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jingfang Huang","raw_affiliation_strings":["Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250"],"raw_orcid":"https://orcid.org/0000-0002-6720-8389","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250","institution_ids":["https://openalex.org/I114027177"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071701467","display_name":"Gary Huber","orcid":"https://orcid.org/0000-0002-5936-6184"},"institutions":[{"id":"https://openalex.org/I1344073410","display_name":"Howard Hughes Medical Institute","ror":"https://ror.org/006w34k90","country_code":"US","type":"facility","lineage":["https://openalex.org/I1344073410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gary Huber","raw_affiliation_strings":["Howard Hughes Medical Institute, University of California at San Diego, La Jolla, CA 92093-0365"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Howard Hughes Medical Institute, University of California at San Diego, La Jolla, CA 92093-0365","institution_ids":["https://openalex.org/I1344073410"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015837947","display_name":"J. Andrew McCammon","orcid":"https://orcid.org/0000-0003-3065-1456"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Andrew McCammon","raw_affiliation_strings":["Department of Chemistry and Biochemistry and Department of Pharmacology, University of California at San Diego, La Jolla, CA 92093-0365"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemistry and Biochemistry and Department of Pharmacology, University of California at San Diego, La Jolla, CA 92093-0365","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015061310","display_name":"B O Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bo Zhang","raw_affiliation_strings":["Center for Research in Extreme Scale Technologies, Indiana University, Bloomington, IN 47404"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Research in Extreme Scale Technologies, Indiana University, Bloomington, IN 47404","institution_ids":["https://openalex.org/I4210119109"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.429,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.68830194,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"40","issue":"3","first_page":"A1345","last_page":"A1361"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9955999851226807,"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":0.9955999851226807,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10490","display_name":"Orbital Angular Momentum in Optics","score":0.9858999848365784,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.7315688133239746},{"id":"https://openalex.org/keywords/orthogonal-matrix","display_name":"Orthogonal matrix","score":0.6714337468147278},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6648837924003601},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6300867199897766},{"id":"https://openalex.org/keywords/orthogonal-complement","display_name":"Orthogonal complement","score":0.5125817656517029},{"id":"https://openalex.org/keywords/orthonormality","display_name":"Orthonormality","score":0.49025991559028625},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.4603360593318939},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44768500328063965},{"id":"https://openalex.org/keywords/transformation-matrix","display_name":"Transformation matrix","score":0.42577752470970154},{"id":"https://openalex.org/keywords/orthogonal-basis","display_name":"Orthogonal basis","score":0.4135698974132538},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3206571936607361},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19724702835083008},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.13319727778434753}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.7315688133239746},{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.6714337468147278},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6648837924003601},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6300867199897766},{"id":"https://openalex.org/C154399039","wikidata":"https://www.wikidata.org/wiki/Q1780921","display_name":"Orthogonal complement","level":3,"score":0.5125817656517029},{"id":"https://openalex.org/C92951342","wikidata":"https://www.wikidata.org/wiki/Q1411166","display_name":"Orthonormality","level":3,"score":0.49025991559028625},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.4603360593318939},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44768500328063965},{"id":"https://openalex.org/C165443888","wikidata":"https://www.wikidata.org/wiki/Q1482183","display_name":"Transformation matrix","level":3,"score":0.42577752470970154},{"id":"https://openalex.org/C187064257","wikidata":"https://www.wikidata.org/wiki/Q3306808","display_name":"Orthogonal basis","level":2,"score":0.4135698974132538},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3206571936607361},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19724702835083008},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.13319727778434753},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"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/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/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/17m1117744","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1117744","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmid:31452593","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/31452593","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM journal on scientific computing : a publication of the Society for Industrial and Applied Mathematics","raw_type":null},{"id":"pmh:oai:escholarship.org:ark:/13030/qt4tk6r7q8","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/4tk6r7q8","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, vol 40, iss 3","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:6709857","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6709857","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM J Sci Comput","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:pubmedcentral.nih.gov:6709857","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6709857","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM J Sci Comput","raw_type":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4974115043","display_name":null,"funder_award_id":"ACI-1440396","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5029780185","display_name":null,"funder_award_id":"GM31749","funder_id":"https://openalex.org/F4320306082","funder_display_name":"Howard Hughes Medical Institute"},{"id":"https://openalex.org/G504002212","display_name":null,"funder_award_id":"DMS-1217080","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7199578972","display_name":null,"funder_award_id":"GM103426","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306082","display_name":"Howard Hughes Medical Institute","ror":"https://ror.org/006w34k90"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W585413735","https://openalex.org/W1569304948","https://openalex.org/W1980705692","https://openalex.org/W1987326264","https://openalex.org/W1988214780","https://openalex.org/W1989925383","https://openalex.org/W1990081118","https://openalex.org/W2018419001","https://openalex.org/W2046058559","https://openalex.org/W2061171222","https://openalex.org/W2083206954","https://openalex.org/W2115003574","https://openalex.org/W2117926105","https://openalex.org/W2123046131","https://openalex.org/W2125439985","https://openalex.org/W2132820941","https://openalex.org/W2151317657","https://openalex.org/W2272815044","https://openalex.org/W2494334047","https://openalex.org/W2606116483","https://openalex.org/W2752638319","https://openalex.org/W3102427576"],"related_works":["https://openalex.org/W3194844793","https://openalex.org/W2805026464","https://openalex.org/W2369726864","https://openalex.org/W2182709136","https://openalex.org/W2128639051","https://openalex.org/W2366652250","https://openalex.org/W1599551753","https://openalex.org/W2075146971","https://openalex.org/W2363331359","https://openalex.org/W4386575044"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,74,121],"apply":[4],"the":[5,18,43,52,69,80,111,140,145],"hierarchical":[6,127],"modeling":[7],"technique":[8],"and":[9,60,67,105,116,142],"study":[10],"some":[11],"numerical":[12,134,146],"linear":[13],"algebra":[14],"problems":[15],"arising":[16],"from":[17],"Brownian":[19],"dynamics":[20],"simulations":[21],"of":[22,31,40,72,87,92,96,144],"biomolecular":[23],"systems":[24],"where":[25,109],"molecules":[26],"are":[27,119,136],"modeled":[28],"as":[29],"ensembles":[30],"rigid":[32,36],"bodies.":[33],"Given":[34],"a":[35],"body":[37],"$p$":[38],"consisting":[39,86],"$n$":[41],"beads,":[42],"$6":[44],"\\times":[45,82],"3n$":[46,83],"transformation":[47],"matrix":[48,84],"$Z$":[49],"that":[50],"maps":[51],"force":[53],"on":[54],"each":[55],"bead":[56],"to":[57,77,138],"$p$'s":[58],"translational":[59],"rotational":[61],"forces":[62],"(a":[63],"$6\\times":[64],"1$":[65],"vector),":[66],"$V$":[68],"row":[70],"space":[71],"$Z$,":[73],"show":[75],"how":[76],"explicitly":[78,130],"construct":[79],"$(3n-6)":[81],"$\\tilde{Q}$":[85],"$(3n-6)$":[88],"orthonormal":[89],"basis":[90],"vectors":[91],"$V^{\\perp}$":[93],"(orthogonal":[94],"complement":[95],"$V$)":[97],"using":[98],"only":[99,110],"$\\mathcal":[100,125],"O(n":[101],"\\log":[102],"n)$":[103],"operations":[104],"storage.":[106],"For":[107],"applications":[108],"matrix-vector":[112],"multiplications":[113],"$\\tilde{Q}\\bf":[114],"V$":[115,118],"$\\tilde{Q}^T\\bf":[117],"needed,":[120],"introduce":[122],"asymptotically":[123],"optimal":[124],"O(n)$":[126],"algorithms":[128],"without":[129],"forming":[131],"$\\tilde{Q}$.":[132],"Preliminary":[133],"results":[135],"presented":[137],"demonstrate":[139],"performance":[141],"accuracy":[143],"algorithms.":[147]},"counts_by_year":[{"year":2019,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
