{"id":"https://openalex.org/W2119759375","doi":"https://doi.org/10.1007/s11075-006-9022-x","title":"Using cross-product matrices to compute the SVD","display_name":"Using cross-product matrices to compute the SVD","publication_year":2006,"publication_date":"2006-05-01","ids":{"openalex":"https://openalex.org/W2119759375","doi":"https://doi.org/10.1007/s11075-006-9022-x","mag":"2119759375"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-006-9022-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-006-9022-x","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/A5075378610","display_name":"Zhongxiao Jia","orcid":"https://orcid.org/0000-0001-9761-8517"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhongxiao Jia","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, PR China","Tsinghua University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, PR China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075378610"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.338,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.63421394,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"42","issue":"1","first_page":"31","last_page":"61"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.8607234954833984},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.8221906423568726},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7430724501609802},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.733195960521698},{"id":"https://openalex.org/keywords/rayleigh-quotient","display_name":"Rayleigh quotient","score":0.6227454543113708},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6152908205986023},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4810517132282257},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4596502482891083},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.41248971223831177},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38800686597824097},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36293482780456543},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19821494817733765}],"concepts":[{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.8607234954833984},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.8221906423568726},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7430724501609802},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.733195960521698},{"id":"https://openalex.org/C2778158742","wikidata":"https://www.wikidata.org/wiki/Q1665115","display_name":"Rayleigh quotient","level":3,"score":0.6227454543113708},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6152908205986023},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4810517132282257},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4596502482891083},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.41248971223831177},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38800686597824097},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36293482780456543},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19821494817733765},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"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/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/s11075-006-9022-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-006-9022-x","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W70219409","https://openalex.org/W658559791","https://openalex.org/W1480928214","https://openalex.org/W1576347883","https://openalex.org/W1596181878","https://openalex.org/W1760551737","https://openalex.org/W1981745143","https://openalex.org/W1986194092","https://openalex.org/W2010315317","https://openalex.org/W2020804487","https://openalex.org/W2024312641","https://openalex.org/W2030827135","https://openalex.org/W2038246004","https://openalex.org/W2064559422","https://openalex.org/W2342316458","https://openalex.org/W2798909945","https://openalex.org/W3022909171","https://openalex.org/W3150353689","https://openalex.org/W4242722506","https://openalex.org/W4301491118","https://openalex.org/W4302564868","https://openalex.org/W4320800818"],"related_works":["https://openalex.org/W4319586039","https://openalex.org/W4382583540","https://openalex.org/W1607100495","https://openalex.org/W2147072251","https://openalex.org/W1990844505","https://openalex.org/W2148568324","https://openalex.org/W4386721910","https://openalex.org/W4378770618","https://openalex.org/W2164147222","https://openalex.org/W3189092169"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
