{"id":"https://openalex.org/W7223069769","doi":"https://doi.org/10.48550/arxiv.2610.25361","title":"Improved algorithms for computing the matrix logarithm based on the double-exponential formula","display_name":"Improved algorithms for computing the matrix logarithm based on the double-exponential formula","publication_year":2026,"publication_date":"2026-10-18","ids":{"openalex":"https://openalex.org/W7223069769","doi":"https://doi.org/10.48550/arxiv.2610.25361"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.25361","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25361","pdf_url":"https://arxiv.org/pdf/2610.25361","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.25361","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085363025","display_name":"Tomoaki Okayama","orcid":"https://orcid.org/0000-0001-9942-1670","observed_orcids":["https://orcid.org/0000-0001-9942-1670"]},"institutions":[{"id":"https://openalex.org/I57930482","display_name":"Hiroshima City University","ror":"https://ror.org/001et4e78","country_code":"JP","type":"education","lineage":["https://openalex.org/I57930482"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Okayama, Tomoaki","raw_affiliation_strings":["Hiroshima City University , 3-4-1 , Ozuka-Higashi , Asaminami-ku , Hiroshima , 731-3194 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hiroshima City University , 3-4-1 , Ozuka-Higashi , Asaminami-ku , Hiroshima , 731-3194 , Japan","institution_ids":["https://openalex.org/I57930482"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159154608","display_name":"Tsubasa Setogawa","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Setogawa, Tsubasa","raw_affiliation_strings":["Daiko Techno Co., Ltd. , Daiko Hiratsuka Building , 1-14 , Higashi-Hiratsuka-cho , Naka-ku , Hiroshima , 730-0025 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Daiko Techno Co., Ltd. , Daiko Hiratsuka Building , 1-14 , Higashi-Hiratsuka-cho , Naka-ku , Hiroshima , 730-0025 , Japan","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9585000276565552,"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":0.9585000276565552,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.014000000432133675,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.008899999782443047,"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/matrix-logarithm","display_name":"matrix logarithm","score":0.9990000128746033},{"id":"https://openalex.org/keywords/double-exponential-formula","display_name":"double exponential formula","score":0.9599999785423279},{"id":"https://openalex.org/keywords/numerical-quadrature","display_name":"numerical quadrature","score":0.6589999794960022},{"id":"https://openalex.org/keywords/adaptive-mesh-refinement","display_name":"adaptive mesh refinement","score":0.7950000166893005},{"id":"https://openalex.org/keywords/nested-grids","display_name":"nested grids","score":0.6809999942779541},{"id":"https://openalex.org/keywords/error-bounds","display_name":"error bounds","score":0.5879999995231628},{"id":"https://openalex.org/keywords/ill-conditioned-matrices","display_name":"ill-conditioned matrices","score":0.9750000238418579},{"id":"https://openalex.org/keywords/gauss-legendre-quadrature","display_name":"Gauss-Legendre quadrature","score":0.7599999904632568},{"id":"https://openalex.org/keywords/matrix-functions","display_name":"matrix functions","score":0.33000001311302185}],"concepts":[{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6825000047683716},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6793000102043152},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6412000060081482},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6291999816894531},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5252000093460083},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.44440001249313354},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44190001487731934},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.43529999256134033},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4327999949455261},{"id":"https://openalex.org/C126148662","wikidata":"https://www.wikidata.org/wiki/Q3890355","display_name":"Discretization error","level":3,"score":0.4065000116825104},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.36970001459121704},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.36880001425743103},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.3499999940395355},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3352000117301941},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.3197000026702881},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.31360000371932983},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.3061000108718872},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.2896000146865845},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2874999940395355},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2685000002384186},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.2671999931335449},{"id":"https://openalex.org/C14103991","wikidata":"https://www.wikidata.org/wiki/Q5527852","display_name":"Gauss\u2013Kronrod quadrature formula","level":4,"score":0.2635999917984009},{"id":"https://openalex.org/C167590341","wikidata":"https://www.wikidata.org/wiki/Q5527850","display_name":"Gauss\u2013Hermite quadrature","level":5,"score":0.25920000672340393},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.25060001015663147}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.25361","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25361","pdf_url":"https://arxiv.org/pdf/2610.25361","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":"doi:10.48550/arxiv.2610.25361","doi":"https://doi.org/10.48550/arxiv.2610.25361","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.25361","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.25361","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25361","pdf_url":"https://arxiv.org/pdf/2610.25361","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223069769.pdf","grobid_xml":"https://content.openalex.org/works/W7223069769.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4415272422"],"related_works":["https://openalex.org/W2970727837","https://openalex.org/W4403790949","https://openalex.org/W7112033207","https://openalex.org/W4386617878","https://openalex.org/W3193402900","https://openalex.org/W7204197986","https://openalex.org/W7099518604","https://openalex.org/W2091491180","https://openalex.org/W2615970112","https://openalex.org/W3163830752"],"abstract_inverted_index":{"Tatsuoka":[0,112],"et":[1,113],"al.":[2],"proposed":[3],"an":[4],"efficient":[5],"algorithm":[6],"for":[7,57],"computing":[8],"the":[9,13,23,41,66,73,95,121],"matrix":[10,83],"logarithm":[11],"using":[12],"double-exponential":[14],"(DE)":[15],"formula.":[16,68],"Its":[17],"discretization":[18],"error":[19,91],"decreases":[20],"exponentially":[21],"as":[22],"number":[24,96],"of":[25,97],"quadrature":[26,56,98],"nodes":[27,99],"grows,":[28],"and":[29,80],"its":[30],"nested":[31],"grids":[32],"allow":[33],"previously":[34,77],"computed":[35,78],"values":[36,79],"to":[37,93],"be":[38],"reused":[39],"when":[40],"mesh":[42,74],"is":[43,51],"refined.":[44],"They":[45],"also":[46],"reported":[47],"that":[48,105],"their":[49],"approach":[50],"more":[52],"robust":[53],"than":[54,111],"Gauss--Legendre":[55],"ill-conditioned":[58],"matrices.":[59],"We":[60],"propose":[61],"two":[62],"algorithms":[63],"based":[64],"on":[65],"DE":[67],"The":[69,86],"first":[70],"adaptively":[71],"refines":[72],"while":[75],"reusing":[76],"requires":[81],"no":[82],"norm":[84],"computations.":[85],"second":[87],"uses":[88],"a":[89,100],"rigorous":[90],"bound":[92],"select":[94],"priori.":[101],"Numerical":[102],"experiments":[103],"show":[104],"both":[106],"methods":[107],"attain":[108],"lower":[109],"errors":[110],"al.'s":[114],"method":[115],"at":[116],"comparable":[117],"elapsed":[118],"times":[119],"over":[120],"tested":[122],"ranges.":[123]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}
