{"id":"https://openalex.org/W2000229183","doi":"https://doi.org/10.1137/s1064827596298257","title":"A Robust, Parallel Homotopy Algorithm for the Symmetric Tridiagonal Eigenproblem","display_name":"A Robust, Parallel Homotopy Algorithm for the Symmetric Tridiagonal Eigenproblem","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2000229183","doi":"https://doi.org/10.1137/s1064827596298257","mag":"2000229183"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827596298257","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827596298257","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5079773481","display_name":"Michael Oettli","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael H. Oettli","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079773481"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.13067034,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"3","first_page":"1016","last_page":"1032"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9994000196456909,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9994000196456909,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9976000189781189,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9975000023841858,"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/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.76078200340271},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.6961425542831421},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6887786388397217},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.560830295085907},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.5466211438179016},{"id":"https://openalex.org/keywords/homotopy-analysis-method","display_name":"Homotopy analysis method","score":0.5116744041442871},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.40259164571762085},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3684545159339905},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3216480612754822},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12612810730934143}],"concepts":[{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.76078200340271},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.6961425542831421},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6887786388397217},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.560830295085907},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.5466211438179016},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.5116744041442871},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.40259164571762085},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3684545159339905},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3216480612754822},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12612810730934143},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1064827596298257","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827596298257","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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":21,"referenced_works":["https://openalex.org/W749397483","https://openalex.org/W1480928214","https://openalex.org/W1491563763","https://openalex.org/W1549777722","https://openalex.org/W1575147392","https://openalex.org/W1580389382","https://openalex.org/W2002739878","https://openalex.org/W2005722356","https://openalex.org/W2009767545","https://openalex.org/W2013737143","https://openalex.org/W2017641901","https://openalex.org/W2045349809","https://openalex.org/W2051717600","https://openalex.org/W2054188927","https://openalex.org/W2059586807","https://openalex.org/W2072396164","https://openalex.org/W2077915982","https://openalex.org/W2089764547","https://openalex.org/W2143628714","https://openalex.org/W2415611842","https://openalex.org/W3022136271"],"related_works":["https://openalex.org/W4212973497","https://openalex.org/W2955221706","https://openalex.org/W1980786482","https://openalex.org/W2360550119","https://openalex.org/W3177208105","https://openalex.org/W3165035967","https://openalex.org/W2389963024","https://openalex.org/W2362256999","https://openalex.org/W2007245702","https://openalex.org/W2048873866"],"abstract_inverted_index":{"The":[0,120],"homotopy":[1,20,96],"method":[2,97],"has":[3],"been":[4],"used":[5],"in":[6,43,88],"the":[7,19,24,64,75,95,112],"past":[8],"for":[9,22,101],"finding":[10],"zeros":[11],"of":[12,52,60,70,74,104],"nonlinear":[13],"functions.":[14],"Early":[15],"algorithms":[16,86],"based":[17,93],"on":[18,94,117,125],"approach":[21],"solving":[23],"symmetric":[25],"eigenproblem":[26],"suffer":[27],"either":[28],"from":[29,36],"insufficient":[30],"orthogonality":[31],"between":[32],"computed":[33],"eigenvectors":[34],"or":[35],"low":[37],"efficiency.":[38],"A":[39,67],"new":[40,76],"algorithm":[41,77,113],"presented":[42],"this":[44],"article":[45,109],"overcomes":[46],"these":[47],"problems":[48],"by":[49,62],"using":[50],"deflation":[51],"close":[53],"eigenpairs":[54],"and":[55,90],"maintains":[56],"a":[57,71],"high":[58],"degree":[59],"parallelism":[61],"applying":[63],"divide-and-conquer":[65],"principle.":[66],"numerical":[68],"comparison":[69],"sequential":[72],"implementation":[73],"shows":[78],"that":[79],"it":[80],"is":[81],"competitive":[82],"with":[83],"other":[84],"well-established":[85],"both":[87],"speed":[89],"accuracy.":[91],"Algorithms":[92],"are":[98,130],"excellent":[99],"candidates":[100],"multicomputers":[102],"because":[103],"their":[105],"natural":[106],"parallelism.":[107],"This":[108],"examines":[110],"how":[111],"can":[114],"be":[115],"implemented":[116],"distributed-memory":[118],"multicomputers.":[119],"experimental":[121],"performance":[122],"results":[123],"obtained":[124],"an":[126],"Intel":[127],"Paragon":[128],"multicomputer":[129],"very":[131],"satisfying.":[132]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}