{"id":"https://openalex.org/W4406957565","doi":"https://doi.org/10.1090/mcom/4074","title":"QQMR: A structure preserving quaternion quasi-minimal residual method","display_name":"QQMR: A structure preserving quaternion quasi-minimal residual method","publication_year":2025,"publication_date":"2025-01-29","ids":{"openalex":"https://openalex.org/W4406957565","doi":"https://doi.org/10.1090/mcom/4074"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4074","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4074","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"preprint","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/A5100455256","display_name":"Tao Li","orcid":"https://orcid.org/0000-0001-8966-7239"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tao Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100771668","display_name":"Qing\u2010Wen Wang","orcid":"https://orcid.org/0000-0003-0189-5355"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qing-Wen Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"95","issue":"358","first_page":"867","last_page":"896"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9943000078201294,"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":0.9943000078201294,"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/T10514","display_name":"Numerical methods in engineering","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9909999966621399,"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/quaternion","display_name":"Quaternion","score":0.8315242528915405},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.8063012361526489},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5816634893417358},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34050875902175903},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3397206664085388},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29727524518966675},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25670260190963745}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.8315242528915405},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.8063012361526489},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5816634893417358},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34050875902175903},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3397206664085388},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29727524518966675},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25670260190963745}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/4074","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4074","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Climate action","score":0.46000000834465027,"id":"https://metadata.un.org/sdg/13"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1973159289","https://openalex.org/W1973310238","https://openalex.org/W1990202535","https://openalex.org/W1993489874","https://openalex.org/W1998366068","https://openalex.org/W2013323650","https://openalex.org/W2033772417","https://openalex.org/W2035080386","https://openalex.org/W2040236138","https://openalex.org/W2044645126","https://openalex.org/W2047552790","https://openalex.org/W2060710554","https://openalex.org/W2065619483","https://openalex.org/W2067152104","https://openalex.org/W2069436097","https://openalex.org/W2085259167","https://openalex.org/W2088116381","https://openalex.org/W2095041371","https://openalex.org/W2117366131","https://openalex.org/W2117686912","https://openalex.org/W2133665775","https://openalex.org/W2151223939","https://openalex.org/W2161469547","https://openalex.org/W2171019910","https://openalex.org/W2262607787","https://openalex.org/W2743597111","https://openalex.org/W2766897841","https://openalex.org/W2810771934","https://openalex.org/W2900180351","https://openalex.org/W2945177740","https://openalex.org/W2948837518","https://openalex.org/W2954665359","https://openalex.org/W2972630054","https://openalex.org/W3114457139","https://openalex.org/W3136981602","https://openalex.org/W3153688434","https://openalex.org/W3184923368","https://openalex.org/W4220955184","https://openalex.org/W4224290667","https://openalex.org/W4231102510","https://openalex.org/W4233520335","https://openalex.org/W4301374466","https://openalex.org/W4318332736","https://openalex.org/W4366000379","https://openalex.org/W4385607572","https://openalex.org/W4391107080","https://openalex.org/W6602670149"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W3127350447","https://openalex.org/W3108700312","https://openalex.org/W4225472102","https://openalex.org/W2382948573","https://openalex.org/W2887325221","https://openalex.org/W2084651007","https://openalex.org/W2184550115"],"abstract_inverted_index":{"The":[0,72,98],"quaternion":[1,11,18,51,58,95],"biconjugate":[2,59],"gradient":[3],"(QBiCG)":[4],"method,":[5],"as":[6],"a":[7,24,33,48],"novel":[8],"variant":[9],"of":[10,70,94,101,118],"Lanczos-type":[12],"methods":[13],"for":[14,90],"solving":[15],"the":[16,30,57,68,79,86,91,109,114,119],"non-Hermitian":[17],"linear":[19,96],"systems,":[20],"does":[21],"not":[22],"yield":[23],"minimization":[25],"property.":[26],"This":[27],"means":[28],"that":[29],"method":[31,54,81,121],"possesses":[32],"rather":[34],"irregular":[35],"convergence":[36,99],"behavior,":[37],"which":[38,66,102],"leads":[39],"to":[40,112],"numerical":[41,110],"instability.":[42],"In":[43],"this":[44],"paper,":[45],"we":[46,107],"propose":[47],"new":[49],"structure-preserving":[50],"quasi-minimal":[52],"residual":[53],"based":[55],"on":[56],"orthonormalization":[60],"procedure":[61],"with":[62,123],"coupled":[63],"two-term":[64],"recurrences,":[65],"overcomes":[67],"drawback":[69],"QBiCG.":[71,124],"computational":[73],"cost":[74],"and":[75,116],"storage":[76],"required":[77],"by":[78],"proposed":[80,120],"are":[82,103],"much":[83],"less":[84],"than":[85],"traditional":[87],"QMR":[88],"iterations":[89],"real":[92],"representation":[93],"systems.":[97],"properties":[100],"also":[104],"established.":[105],"Finally,":[106],"report":[108],"results":[111],"show":[113],"robustness":[115],"effectiveness":[117],"compared":[122]},"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":4}],"updated_date":"2026-08-29T07:29:34.045763","created_date":"2025-10-10T00:00:00"}