{"id":"https://openalex.org/W3202996579","doi":"https://doi.org/10.1137/21m1450197","title":"A General Alternating-Direction Implicit Framework with Gaussian Process Regression Parameter Prediction for Large Sparse Linear Systems","display_name":"A General Alternating-Direction Implicit Framework with Gaussian Process Regression Parameter Prediction for Large Sparse Linear Systems","publication_year":2022,"publication_date":"2022-07-07","ids":{"openalex":"https://openalex.org/W3202996579","doi":"https://doi.org/10.1137/21m1450197","mag":"3202996579"},"language":"en","primary_location":{"id":"doi:10.1137/21m1450197","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1450197","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"],"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/A5101621262","display_name":"Kai Jiang","orcid":"https://orcid.org/0000-0001-9921-2043"},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]},{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai Jiang","raw_affiliation_strings":["Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education,","Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, China, 411105"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education,","institution_ids":[]},{"raw_affiliation_string":"Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, China, 411105","institution_ids":["https://openalex.org/I121296143","https://openalex.org/I4610292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039817063","display_name":"Xuehong Su","orcid":null},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]},{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuehong Su","raw_affiliation_strings":["Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education,","Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, China, 411105"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education,","institution_ids":[]},{"raw_affiliation_string":"Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, China, 411105","institution_ids":["https://openalex.org/I121296143","https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058718871","display_name":"Juan Zhang","orcid":"https://orcid.org/0000-0002-7814-486X"},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]},{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Juan Zhang","raw_affiliation_strings":["Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, China, 411105","Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education,"],"raw_orcid":"https://orcid.org/0000-0002-7814-486X","affiliations":[{"raw_affiliation_string":"Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, China, 411105","institution_ids":["https://openalex.org/I121296143","https://openalex.org/I4610292"]},{"raw_affiliation_string":"Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education,","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0622,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.77872637,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"44","issue":"4","first_page":"A1960","last_page":"A1988"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.996399998664856,"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":0.996399998664856,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.5136207938194275},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.47089532017707825},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.466916561126709},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4538411796092987},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45214778184890747},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3910064101219177},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.3909480571746826},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3883257806301117},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10597971081733704}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5136207938194275},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.47089532017707825},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.466916561126709},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4538411796092987},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45214778184890747},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3910064101219177},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3909480571746826},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3883257806301117},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10597971081733704},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1450197","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1450197","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1607741323","display_name":"\u57fa\u4e8eRiccati\u65b9\u7a0b\u548cLMI\u7684\u63a7\u5236\u7cfb\u7edf\u9c81\u68d2\u7a33\u5b9a\u6027\u7814\u7a76","funder_award_id":"11771370","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2175534321","display_name":null,"funder_award_id":"2021JJ10037","funder_id":"https://openalex.org/F4320330215","funder_display_name":"Natural Science Foundation for Distinguished Young Scholars of Hunan Province"},{"id":"https://openalex.org/G6508579496","display_name":null,"funder_award_id":"19A500","funder_id":"https://openalex.org/F4320311213","funder_display_name":"Education Department of Hunan Province"},{"id":"https://openalex.org/G6960247750","display_name":null,"funder_award_id":"2021JJ10037","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G7329969484","display_name":null,"funder_award_id":"12171412","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320311213","display_name":"Education Department of Hunan Province","ror":"https://ror.org/05ckg3w11"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null},{"id":"https://openalex.org/F4320330215","display_name":"Natural Science Foundation for Distinguished Young Scholars of Hunan Province","ror":null},{"id":"https://openalex.org/F4320330356","display_name":"Distinguished Young Scholar Foundation of Hunan Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W85719053","https://openalex.org/W1259818010","https://openalex.org/W1480376833","https://openalex.org/W1533471646","https://openalex.org/W1964400575","https://openalex.org/W1969810270","https://openalex.org/W1995897527","https://openalex.org/W2002102128","https://openalex.org/W2003372231","https://openalex.org/W2019569173","https://openalex.org/W2024976895","https://openalex.org/W2037939967","https://openalex.org/W2043857934","https://openalex.org/W2043875119","https://openalex.org/W2053564565","https://openalex.org/W2058532290","https://openalex.org/W2075227634","https://openalex.org/W2092803270","https://openalex.org/W2095036901","https://openalex.org/W2095485006","https://openalex.org/W2107386393","https://openalex.org/W2136556155","https://openalex.org/W2168690621","https://openalex.org/W2168947999","https://openalex.org/W2785011264","https://openalex.org/W2972556093","https://openalex.org/W3035235874","https://openalex.org/W3103984481","https://openalex.org/W3140368695","https://openalex.org/W3200756715"],"related_works":["https://openalex.org/W2140288152","https://openalex.org/W2963637926","https://openalex.org/W2799769525","https://openalex.org/W2048140462","https://openalex.org/W1966851638","https://openalex.org/W2101272603","https://openalex.org/W2114279993","https://openalex.org/W2075252297","https://openalex.org/W1964286703","https://openalex.org/W2169866437"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"an":[3],"efficient":[4],"general":[5],"alternating-direction":[6],"implicit":[7],"(GADI)":[8],"framework":[9,22,40,155],"for":[10],"solving":[11],"large":[12],"sparse":[13],"linear":[14,113,199],"systems.":[15],"The":[16,81],"convergence":[17],"property":[18],"of":[19,26,145,161,181],"the":[20,34,38,48,54,62,70,75,93,129,143,153,164,179],"GADI":[21,39,76],"is":[23,51,156,187],"discussed.":[24],"Most":[25],"existing":[27,165,203],"ADI":[28,44,166,204],"methods":[29,176,194,205],"can":[30,41,97,195],"be":[31],"unified":[32],"in":[33,177],"developed":[35],"framework.":[36],"Meanwhile":[37],"derive":[42],"new":[43],"methods.":[45,148],"Moreover,":[46],"as":[47,169],"algorithm":[49],"efficiency":[50],"sensitive":[52],"to":[53,73,91,110,141,159],"splitting":[55,100,174,185],"parameters,":[56,101],"we":[57,127],"offer":[58],"a":[59,86,116,190],"data-driven":[60],"approach,":[61],"Gaussian":[63],"process":[64],"regression":[65,94],"(GPR)":[66],"method":[67,83],"based":[68],"on":[69],"Bayesian":[71],"inference,":[72],"predict":[74,98],"framework's":[77],"relatively":[78,183],"optimal":[79,184],"parameters.":[80],"GPR":[82],"only":[84],"requires":[85],"small":[87],"training":[88],"data":[89],"set":[90],"learn":[92],"prediction":[95],"mapping,":[96],"accurate":[99],"and":[102,119,136,172],"has":[103],"high":[104],"generalization":[105],"capability.":[106],"It":[107],"allows":[108],"us":[109],"efficiently":[111],"solve":[112,196],"systems":[114,200],"with":[115],"one-shot":[117],"computation,":[118],"does":[120],"not":[121,207],"require":[122],"any":[123],"repeated":[124],"computations.":[125],"Finally,":[126],"use":[128],"three-dimensional":[130],"convection-diffusion":[131],"equation,":[132,135],"two-dimensional":[133],"parabolic":[134],"continuous":[137],"Sylvester":[138],"matrix":[139],"equation":[140],"examine":[142],"performance":[144],"our":[146,192],"proposed":[147,154,193],"Numerical":[149],"results":[150],"demonstrate":[151],"that":[152],"faster":[157],"tens":[158],"thousands":[160],"times":[162],"than":[163],"methods,":[167],"such":[168],"(inexact)":[170],"Hermitian":[171],"skew-Hermitian":[173],"type":[175],"which":[178,201],"consumption":[180],"obtaining":[182],"parameters":[186],"ignored.":[188],"As":[189],"result,":[191],"much":[197],"larger":[198],"these":[202],"have":[206],"reached.":[208]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-26T07:53:14.480251","created_date":"2025-10-10T00:00:00"}