{"id":"https://openalex.org/W3170352390","doi":"https://doi.org/10.1137/21m1436774","title":"Cross-Interactive Residual Smoothing for Global and Block Lanczos-Type Solvers for Linear Systems with Multiple Right-Hand Sides","display_name":"Cross-Interactive Residual Smoothing for Global and Block Lanczos-Type Solvers for Linear Systems with Multiple Right-Hand Sides","publication_year":2022,"publication_date":"2022-08-08","ids":{"openalex":"https://openalex.org/W3170352390","doi":"https://doi.org/10.1137/21m1436774","mag":"3170352390"},"language":"en","primary_location":{"id":"doi:10.1137/21m1436774","is_oa":true,"landing_page_url":"https://doi.org/10.1137/21m1436774","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1137/21m1436774","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076562311","display_name":"Kensuke Aihara","orcid":"https://orcid.org/0000-0002-4802-4090"},"institutions":[{"id":"https://openalex.org/I185088104","display_name":"Tokyo City University","ror":"https://ror.org/04dt6bw53","country_code":"JP","type":"education","lineage":["https://openalex.org/I185088104"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Kensuke Aihara","raw_affiliation_strings":["Tokyo city university"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tokyo city university","institution_ids":["https://openalex.org/I185088104"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047435295","display_name":"Akira Imakura","orcid":null},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Akira Imakura","raw_affiliation_strings":["University OF Tsukuba"],"raw_orcid":"https://orcid.org/0000-0003-4994-2499","affiliations":[{"raw_affiliation_string":"University OF Tsukuba","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034814306","display_name":"Keiichi Morikuni","orcid":null},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Keiichi Morikuni","raw_affiliation_strings":["University OF Tsukuba"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University OF Tsukuba","institution_ids":["https://openalex.org/I146399215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5076562311"],"corresponding_institution_ids":["https://openalex.org/I185088104"],"apc_list":null,"apc_paid":null,"fwci":0.4525,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63127659,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"43","issue":"3","first_page":"1308","last_page":"1330"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/residual","display_name":"Residual","score":0.9076159596443176},{"id":"https://openalex.org/keywords/lanczos-resampling","display_name":"Lanczos resampling","score":0.8013705015182495},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.7968518733978271},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.7474879622459412},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.6521539688110352},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6090573668479919},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5618856549263},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5075808763504028},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4892863929271698},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4359409213066101},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4269484281539917},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.34432870149612427},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3334652781486511},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.16597336530685425},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08166685700416565},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07942548394203186}],"concepts":[{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.9076159596443176},{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.8013705015182495},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.7968518733978271},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.7474879622459412},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.6521539688110352},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6090573668479919},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5618856549263},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5075808763504028},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4892863929271698},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4359409213066101},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4269484281539917},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.34432870149612427},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3334652781486511},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.16597336530685425},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08166685700416565},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07942548394203186},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/21m1436774","is_oa":true,"landing_page_url":"https://doi.org/10.1137/21m1436774","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2106.00284","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.00284","pdf_url":"https://arxiv.org/pdf/2106.00284","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"}],"best_oa_location":{"id":"doi:10.1137/21m1436774","is_oa":true,"landing_page_url":"https://doi.org/10.1137/21m1436774","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1423185572","display_name":null,"funder_award_id":"JP21K11925","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G1562135409","display_name":null,"funder_award_id":"JP16K17639","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G2078760851","display_name":null,"funder_award_id":"JP19KK0255","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G2447242860","display_name":null,"funder_award_id":"JP17K12690","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3839096797","display_name":null,"funder_award_id":"JP18K18064","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4477793024","display_name":null,"funder_award_id":"JP20K14356","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8211505071","display_name":null,"funder_award_id":"JP21H03451","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8602431023","display_name":null,"funder_award_id":"JP18H03250","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":27,"referenced_works":["https://openalex.org/W263597469","https://openalex.org/W1496910322","https://openalex.org/W1706978965","https://openalex.org/W1964233075","https://openalex.org/W1970855940","https://openalex.org/W1985536181","https://openalex.org/W2018784891","https://openalex.org/W2020804487","https://openalex.org/W2027903448","https://openalex.org/W2031968565","https://openalex.org/W2035080386","https://openalex.org/W2038496569","https://openalex.org/W2040425799","https://openalex.org/W2041588636","https://openalex.org/W2051270844","https://openalex.org/W2083720901","https://openalex.org/W2155216327","https://openalex.org/W2163612185","https://openalex.org/W2164088261","https://openalex.org/W2171592720","https://openalex.org/W2724407126","https://openalex.org/W2781510024","https://openalex.org/W2925692864","https://openalex.org/W3005534689","https://openalex.org/W3022909171","https://openalex.org/W3090724082","https://openalex.org/W4206119392"],"related_works":["https://openalex.org/W4299721875","https://openalex.org/W3170352390","https://openalex.org/W2038323838","https://openalex.org/W2789837637","https://openalex.org/W1596734974","https://openalex.org/W591632009","https://openalex.org/W2009567814","https://openalex.org/W2076138765","https://openalex.org/W1976157534","https://openalex.org/W2147279877"],"abstract_inverted_index":{"Global":[0],"and":[1,33,91,97,162],"block":[2,22],"Krylov":[3],"subspace":[4],"methods":[5,134],"are":[6],"efficient":[7],"iterative":[8],"solvers":[9,24],"for":[10,76],"large":[11,27,37],"sparse":[12],"linear":[13,125],"systems":[14,126],"with":[15,127,140],"multiple":[16,128],"right-hand":[17,129],"sides.":[18,130],"However,":[19],"global":[20],"or":[21],"Lanczos-type":[23,79],"often":[25],"exhibit":[26],"oscillations":[28,56],"in":[29],"the":[30,42,48,60,70,73,89,95,104,111,121,137,152,155],"residual":[31,38,51,66,118,138],"norms":[32],"may":[34],"have":[35],"a":[36,64,141],"gap":[39,139],"relating":[40],"to":[41,120,146],"loss":[43],"of":[44,47,72,84,94,107,123,154],"attainable":[45,61,74],"accuracy":[46,75],"approximations.":[49],"Conventional":[50],"smoothing":[52,67,119],"schemes":[53],"suppress":[54],"these":[55],"but":[57],"cannot":[58],"improve":[59],"accuracy,":[62],"whereas":[63],"recent":[65],"scheme":[68,86],"enables":[69],"improvement":[71],"single":[77],"right-hand-side":[78],"solvers.":[80],"The":[81,131],"underlying":[82],"concept":[83],"this":[85,116],"is":[87],"that":[88],"primary":[90],"smoothed":[92,133],"sequences":[93],"approximations":[96],"residuals":[98],"influence":[99],"one":[100],"another,":[101],"thereby":[102],"avoiding":[103],"severe":[105],"propagation":[106],"rounding":[108,159],"errors.":[109],"In":[110],"present":[112],"study,":[113],"we":[114],"extend":[115],"cross-interactive":[117],"case":[122],"solving":[124],"resulting":[132],"can":[135],"reduce":[136],"low":[142],"additional":[143],"cost":[144],"compared":[145],"their":[147],"original":[148],"counterparts.":[149],"We":[150],"demonstrate":[151],"effectiveness":[153],"proposed":[156],"approach":[157],"through":[158],"error":[160],"analysis":[161],"numerical":[163],"experiments.":[164]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}