{"id":"https://openalex.org/W2495415857","doi":"https://doi.org/10.1145/2930889.2930905","title":"System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions","display_name":"System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions","publication_year":2016,"publication_date":"2016-07-19","ids":{"openalex":"https://openalex.org/W2495415857","doi":"https://doi.org/10.1145/2930889.2930905","mag":"2495415857"},"language":"en","primary_location":{"id":"doi:10.1145/2930889.2930905","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2930889.2930905","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"conference-paper","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/A5024995691","display_name":"Masayuki Noro","orcid":"https://orcid.org/0009-0003-4953-8258"},"institutions":[{"id":"https://openalex.org/I133557312","display_name":"Rikkyo University","ror":"https://ror.org/00x194q47","country_code":"JP","type":"education","lineage":["https://openalex.org/I133557312"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masayuki Noro","raw_affiliation_strings":["Rikkyo University, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rikkyo University, Tokyo, Japan","institution_ids":["https://openalex.org/I133557312"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5024995691"],"corresponding_institution_ids":["https://openalex.org/I133557312"],"apc_list":null,"apc_paid":null,"fwci":1.3333,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.7923445,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"381","last_page":"388"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9970999956130981,"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"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9970999956130981,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.991599977016449,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7496852278709412},{"id":"https://openalex.org/keywords/wishart-distribution","display_name":"Wishart distribution","score":0.5952940583229065},{"id":"https://openalex.org/keywords/hypergeometric-function-of-a-matrix-argument","display_name":"Hypergeometric function of a matrix argument","score":0.5311877727508545},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.5171829462051392},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5103463530540466},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.5021259784698486},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.49775150418281555},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44561317563056946},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.44503605365753174},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44225749373435974},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4399052560329437},{"id":"https://openalex.org/keywords/matrix-function","display_name":"Matrix function","score":0.43299829959869385},{"id":"https://openalex.org/keywords/confluent-hypergeometric-function","display_name":"Confluent hypergeometric function","score":0.41333654522895813},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40332335233688354},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.38892918825149536},{"id":"https://openalex.org/keywords/hypergeometric-function","display_name":"Hypergeometric function","score":0.31816399097442627},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.11025118827819824},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09110915660858154},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08081430196762085}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7496852278709412},{"id":"https://openalex.org/C33962027","wikidata":"https://www.wikidata.org/wiki/Q1930697","display_name":"Wishart distribution","level":3,"score":0.5952940583229065},{"id":"https://openalex.org/C165175332","wikidata":"https://www.wikidata.org/wiki/Q5958021","display_name":"Hypergeometric function of a matrix argument","level":4,"score":0.5311877727508545},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5171829462051392},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5103463530540466},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.5021259784698486},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.49775150418281555},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44561317563056946},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.44503605365753174},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44225749373435974},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4399052560329437},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.43299829959869385},{"id":"https://openalex.org/C148160416","wikidata":"https://www.wikidata.org/wiki/Q783948","display_name":"Confluent hypergeometric function","level":3,"score":0.41333654522895813},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40332335233688354},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.38892918825149536},{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.31816399097442627},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.11025118827819824},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09110915660858154},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08081430196762085},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2930889.2930905","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2930889.2930905","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1220874193","display_name":"Efficient methods for Groebner basis computation, verification and thier applications","funder_award_id":"15K05008","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G2117073463","display_name":"Developments in Interactions between Algebraic Geometry and Integrable Systems","funder_award_id":"24224001","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1627130614","https://openalex.org/W1969213662","https://openalex.org/W1973330503","https://openalex.org/W2014999546","https://openalex.org/W2015932327","https://openalex.org/W2027616605","https://openalex.org/W2107704778","https://openalex.org/W2120350343","https://openalex.org/W2963973710","https://openalex.org/W4293005804","https://openalex.org/W4300831640","https://openalex.org/W4362230038"],"related_works":["https://openalex.org/W3175924828","https://openalex.org/W2952141971","https://openalex.org/W2037695323","https://openalex.org/W2027616605","https://openalex.org/W3112880391","https://openalex.org/W2408146013","https://openalex.org/W3095321705","https://openalex.org/W4399170414","https://openalex.org/W3013955663","https://openalex.org/W3013008973"],"abstract_inverted_index":{"The":[0,66],"hypergeometric":[1],"function":[2,13,25],"1F1":[3,59,82,167,185,217],"of":[4,18,26,30,73,110,147,161,177,180,191,212,221,242],"a":[5,10,31,178,183,210,215,239],"matrix":[6,33,58,81,166],"argument":[7],"Y":[8],"is":[9,38,68,186],"symmetric":[11],"entire":[12],"in":[14,22,40,130],"the":[15,23,27,57,61,71,80,96,100,108,115,131,145,165,175,189,192,197,202,219],"eigenvalues":[16],"y1,...,ym":[17],"Y.":[19],"It":[20],"appears":[21],"distribution":[24,42],"largest":[28],"eigenvalue":[29],"Wishart":[32],"and":[34,90,247],"its":[35],"numerical":[36,251],"evaluation":[37],"important":[39],"multivariate":[41],"theory.":[43],"Hashiguchi":[44,118],"et":[45,119],"al.":[46,120],"(J.":[47],"Multivariate":[48],"Analysis,":[49],"2013)":[50],"proposed":[51],"an":[52,122,230],"efficient":[53],"algorithm":[54,67],"for":[55,149,158,168,182,214,232,244],"evaluating":[56],"by":[60,79,84,128,140,164],"holonomic":[62],"gradient":[63],"method":[64],"(HGM).":[65],"based":[69],"on":[70,114],"system":[72,109,146,179,211],"partial":[74],"differential":[75,124],"equations":[76],"(PDEs)":[77],"satisfied":[78,127,163],"given":[83],"Muirhead":[85],"(Ann.":[86],"Math.":[87],"Statist.,":[88],"1970)":[89],"it":[91],"cannot":[92],"be":[93],"applied":[94],"to":[95,144,188,235],"diagonal":[97,116,223,245],"cases,":[98],"i.e.":[99],"cases":[101,246],"where":[102],"several":[103],"yi's":[104],"are":[105,138],"equal":[106],"because":[107],"PDEs":[111,148,162,181,213],"has":[112],"singularities":[113],"region.":[117],"derived":[121,195],"ordinary":[123],"equation":[125],"(ODE)":[126],"1F1(y,y)":[129],"bivariate":[132],"case":[133],"from":[134,196],"some":[135,250],"relations":[136],"which":[137],"obtained":[139],"applying":[141],"l'opital":[142],"rule":[143],"1F1(y1,y2).":[150],"In":[151],"this":[152,156],"paper":[153],"we":[154,205,248],"generalize":[155],"approach":[157],"computing":[159],"systems":[160],"various":[169],"diagonalization":[170,198],"patterns.":[171],"We":[172,227,237],"show":[173,206,249],"that":[174,207],"existence":[176],"diagonalized":[184,216],"reduced":[187],"non-singularity":[190,203],"matrices":[193],"systematically":[194],"pattern.":[199],"By":[200],"checking":[201],"numerically,":[204],"there":[208],"exists":[209],"if":[218],"size":[220],"each":[222],"block":[224],"\u2264":[225],"36.":[226],"have":[228],"computed":[229],"ODE":[231],"1F1(y,...,y)":[233],"up":[234],"m=22.":[236],"made":[238],"test":[240],"implementation":[241],"HGM":[243],"results.":[252]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}