{"id":"https://openalex.org/W2042603350","doi":"https://doi.org/10.1080/00207160310001650134","title":"An iterative algorithm for approximate orthogonalisation of symmetric matrices","display_name":"An iterative algorithm for approximate orthogonalisation of symmetric matrices","publication_year":2004,"publication_date":"2004-02-01","ids":{"openalex":"https://openalex.org/W2042603350","doi":"https://doi.org/10.1080/00207160310001650134","mag":"2042603350"},"language":"en","primary_location":{"id":"doi:10.1080/00207160310001650134","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160310001650134","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5021181231","display_name":"Marcus Mohr","orcid":"https://orcid.org/0000-0003-2942-8484"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. Mohr","raw_affiliation_strings":["Lehrstuhl f\u00fcr Sensorik , Friedrich-Alexander-University of Erlangen-Nuremberg , Paul-Gordan-Stra\u00dfe 3/5, Erlangen, Germany , D-91052"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl f\u00fcr Sensorik , Friedrich-Alexander-University of Erlangen-Nuremberg , Paul-Gordan-Stra\u00dfe 3/5, Erlangen, Germany , D-91052","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001697008","display_name":"Constantin Popa","orcid":"https://orcid.org/0000-0002-4318-7501"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"C. Popa","raw_affiliation_strings":["Lehrstuhl f\u00fcr Informatik 10 (Systemsimulation) , Friedrich-Alexander-University of Erlangen\u2013Nuremberg , Cauerstrasse 6, D-91058, Erlangen, Germany"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl f\u00fcr Informatik 10 (Systemsimulation) , Friedrich-Alexander-University of Erlangen\u2013Nuremberg , Cauerstrasse 6, D-91058, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109197540","display_name":"Ulrich R\u00fcde","orcid":null},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"U. R\u00fcde","raw_affiliation_strings":["Lehrstuhl f\u00fcr Informatik 10 (Systemsimulation) , Friedrich-Alexander-University of Erlangen\u2013Nuremberg , Cauerstrasse 6, D-91058, Erlangen, Germany"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl f\u00fcr Informatik 10 (Systemsimulation) , Friedrich-Alexander-University of Erlangen\u2013Nuremberg , Cauerstrasse 6, D-91058, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001697008"],"corresponding_institution_ids":["https://openalex.org/I181369854"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.13658405,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"81","issue":"2","first_page":"215","last_page":"226"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9907000064849854,"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/mathematics","display_name":"Mathematics","score":0.7339943647384644},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6271485090255737},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5999038815498352},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5542457103729248},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5322200059890747},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5173782110214233},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5065973997116089},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5016083717346191},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4779339134693146},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20142820477485657},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18733295798301697}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7339943647384644},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6271485090255737},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5999038815498352},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5542457103729248},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5322200059890747},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5173782110214233},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5065973997116089},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5016083717346191},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4779339134693146},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20142820477485657},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18733295798301697},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207160310001650134","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160310001650134","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.331.9143","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.9143","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www10.informatik.uni-erlangen.de/Publications/TechnicalReports/TechRep03-2.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1594234351","https://openalex.org/W1963702777","https://openalex.org/W2010855047","https://openalex.org/W2056633351","https://openalex.org/W2140064412","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W2370840338","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W2022062253"],"abstract_inverted_index":{"In":[0,25,74],"a":[1,31,102,113,117],"previous":[2,93],"article,":[3,28,80],"one":[4],"of":[5,11,34,40,78,116],"the":[6,26,38,48,58,75,79,87,92],"authors":[7],"presented":[8,111],"an":[9,12,68],"extension":[10,36],"iterative":[13],"approximate":[14],"orthogonalisation":[15],"algorithm,":[16,47],"due":[17],"to":[18],"Z.":[19],"Kovarik,":[20],"for":[21,37,57,112],"arbitrary":[22,41],"rectangular":[23],"matrices.":[24,43],"present":[27],"we":[29,81,84],"propose":[30],"modified":[32],"version":[33],"this":[35,45],"class":[39],"symmetric":[42],"For":[44],"new":[46],"computational":[49],"effort":[50],"per":[51,72],"iteration":[52],"is":[53],"much":[54],"smaller":[55],"than":[56],"initial":[59],"one.":[60],"We":[61],"prove":[62],"its":[63],"convergence":[64],"and":[65],"also":[66,110],"derive":[67],"error":[69],"reduction":[70],"factor":[71],"iteration.":[73],"second":[76],"part":[77],"show":[82],"that":[83],"can":[85],"eliminate":[86],"matrix":[88,104],"inversion":[89],"required":[90],"by":[91,98],"algorithm":[94],"in":[95],"each":[96],"iteration,":[97],"replacing":[99],"it":[100],"with":[101],"polynomial":[103],"expression.":[105],"Some":[106],"numerical":[107],"experiments":[108],"are":[109],"collocation":[114],"discretisation":[115],"first":[118],"kind":[119],"integral":[120],"equation.":[121]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
