{"id":"https://openalex.org/W4405986092","doi":"https://doi.org/10.1007/s11075-024-02002-8","title":"The backward rounding error analysis of the quaternion Givens QR decomposition","display_name":"The backward rounding error analysis of the quaternion Givens QR decomposition","publication_year":2025,"publication_date":"2025-01-02","ids":{"openalex":"https://openalex.org/W4405986092","doi":"https://doi.org/10.1007/s11075-024-02002-8"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-024-02002-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-024-02002-8","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5053047087","display_name":"Fengxia Zhang","orcid":"https://orcid.org/0000-0002-9574-8155"},"institutions":[{"id":"https://openalex.org/I196934937","display_name":"Liaocheng University","ror":"https://ror.org/03yh0n709","country_code":"CN","type":"education","lineage":["https://openalex.org/I196934937"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fengxia Zhang","raw_affiliation_strings":["College of Mathematical Science, Liaocheng University, Liaocheng, 252000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematical Science, Liaocheng University, Liaocheng, 252000, China","institution_ids":["https://openalex.org/I196934937"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015051319","display_name":"Yuqing Zhang","orcid":"https://orcid.org/0000-0001-7954-1149"},"institutions":[{"id":"https://openalex.org/I196934937","display_name":"Liaocheng University","ror":"https://ror.org/03yh0n709","country_code":"CN","type":"education","lineage":["https://openalex.org/I196934937"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuqing Zhang","raw_affiliation_strings":["College of Mathematical Science, Liaocheng University, Liaocheng, 252000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematical Science, Liaocheng University, Liaocheng, 252000, China","institution_ids":["https://openalex.org/I196934937"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101957752","display_name":"Zhihan Zhou","orcid":"https://orcid.org/0000-0002-9475-465X"},"institutions":[{"id":"https://openalex.org/I196934937","display_name":"Liaocheng University","ror":"https://ror.org/03yh0n709","country_code":"CN","type":"education","lineage":["https://openalex.org/I196934937"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhihan Zhou","raw_affiliation_strings":["College of Mathematical Science, Liaocheng University, Liaocheng, 252000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematical Science, Liaocheng University, Liaocheng, 252000, China","institution_ids":["https://openalex.org/I196934937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5106381930","display_name":"Musheng Wei","orcid":null},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Musheng Wei","raw_affiliation_strings":["College of Mathematics and Science, Shanghai Normal University, Shanghai, 200234, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Science, Shanghai Normal University, Shanghai, 200234, China","institution_ids":["https://openalex.org/I21945476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5053047087"],"corresponding_institution_ids":["https://openalex.org/I196934937"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.3645,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.88980542,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"101","issue":"1","first_page":"199","last_page":"220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.988099992275238,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.781219482421875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7317661643028259},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.7147150039672852},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5051723122596741},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.46875929832458496},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.4337661862373352},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3412683606147766},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3207651972770691},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.31582891941070557},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22848382592201233},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14415809512138367},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1439031958580017},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.13423588871955872},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07478353381156921}],"concepts":[{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.781219482421875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7317661643028259},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.7147150039672852},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5051723122596741},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.46875929832458496},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.4337661862373352},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3412683606147766},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3207651972770691},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.31582891941070557},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22848382592201233},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14415809512138367},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1439031958580017},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.13423588871955872},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07478353381156921},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-024-02002-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-024-02002-8","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","score":0.46000000834465027,"display_name":"Climate action"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W2020804487","https://openalex.org/W2073961410","https://openalex.org/W2170240836","https://openalex.org/W2313568242","https://openalex.org/W2318781916","https://openalex.org/W2329857273","https://openalex.org/W2517407553","https://openalex.org/W2595114961","https://openalex.org/W2743597111","https://openalex.org/W2794633610","https://openalex.org/W2898211903","https://openalex.org/W2909969574","https://openalex.org/W3016575267","https://openalex.org/W3098972513","https://openalex.org/W3101810314","https://openalex.org/W3136981602","https://openalex.org/W4281478956","https://openalex.org/W4285288115","https://openalex.org/W4309236692","https://openalex.org/W4319588361","https://openalex.org/W4367301784","https://openalex.org/W4376278798","https://openalex.org/W4386523188","https://openalex.org/W4386571691","https://openalex.org/W4388997055","https://openalex.org/W4395075442"],"related_works":["https://openalex.org/W2156629920","https://openalex.org/W2021455005","https://openalex.org/W2383134623","https://openalex.org/W2063857110","https://openalex.org/W3211499886","https://openalex.org/W2485409430","https://openalex.org/W2504297729","https://openalex.org/W2099163195","https://openalex.org/W1490938129","https://openalex.org/W2034998146"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-10T08:33:47.465468","created_date":"2025-10-10T00:00:00"}