{"id":"https://openalex.org/W2006918424","doi":"https://doi.org/10.1007/bf02140775","title":"Homotopy method for the numerical solution of the eigenvalue problem of self-adjoint partial differential operators","display_name":"Homotopy method for the numerical solution of the eigenvalue problem of self-adjoint partial differential operators","publication_year":1995,"publication_date":"1995-09-01","ids":{"openalex":"https://openalex.org/W2006918424","doi":"https://doi.org/10.1007/bf02140775","mag":"2006918424"},"language":"en","primary_location":{"id":"doi:10.1007/bf02140775","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02140775","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/A5003813327","display_name":"S. H. Lui","orcid":"https://orcid.org/0000-0003-2024-5817"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"S. H. Lui","raw_affiliation_strings":["Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong","Department of Mathematics Hong Kong University of Science and Technology Kowloon, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"Department of Mathematics Hong Kong University of Science and Technology Kowloon, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110003399","display_name":"Gene H. Golub","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G. H. Golub","raw_affiliation_strings":["Computer Science Department, Stanford University, 94305-2140, Stanford, CA, USA","Computer Science Department, Stanford University Stanford, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, Stanford University, 94305-2140, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Computer Science Department, Stanford University Stanford, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.0682,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.75052773,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"2","first_page":"363","last_page":"378"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9991999864578247,"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":0.8758231997489929},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7655724883079529},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5051026940345764},{"id":"https://openalex.org/keywords/homotopy-analysis-method","display_name":"Homotopy analysis method","score":0.47500836849212646},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45665255188941956},{"id":"https://openalex.org/keywords/inverse-iteration","display_name":"Inverse iteration","score":0.4485177993774414},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.44298285245895386},{"id":"https://openalex.org/keywords/eigenvalue-perturbation","display_name":"Eigenvalue perturbation","score":0.44271862506866455},{"id":"https://openalex.org/keywords/rayleigh-quotient","display_name":"Rayleigh quotient","score":0.43655988574028015},{"id":"https://openalex.org/keywords/matrix-differential-equation","display_name":"Matrix differential equation","score":0.4292267858982086},{"id":"https://openalex.org/keywords/defective-matrix","display_name":"Defective matrix","score":0.42468926310539246},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4110088348388672},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.3499090373516083},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2882322669029236},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24748393893241882},{"id":"https://openalex.org/keywords/diagonalizable-matrix","display_name":"Diagonalizable matrix","score":0.2406400442123413},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.17117521166801453}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8758231997489929},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7655724883079529},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5051026940345764},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.47500836849212646},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45665255188941956},{"id":"https://openalex.org/C2505209","wikidata":"https://www.wikidata.org/wiki/Q1671724","display_name":"Inverse iteration","level":3,"score":0.4485177993774414},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.44298285245895386},{"id":"https://openalex.org/C46865736","wikidata":"https://www.wikidata.org/wiki/Q5348914","display_name":"Eigenvalue perturbation","level":3,"score":0.44271862506866455},{"id":"https://openalex.org/C2778158742","wikidata":"https://www.wikidata.org/wiki/Q1665115","display_name":"Rayleigh quotient","level":3,"score":0.43655988574028015},{"id":"https://openalex.org/C105671362","wikidata":"https://www.wikidata.org/wiki/Q6787870","display_name":"Matrix differential equation","level":3,"score":0.4292267858982086},{"id":"https://openalex.org/C36967811","wikidata":"https://www.wikidata.org/wiki/Q5251123","display_name":"Defective matrix","level":5,"score":0.42468926310539246},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4110088348388672},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.3499090373516083},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2882322669029236},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24748393893241882},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.2406400442123413},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.17117521166801453},{"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:10.1007/bf02140775","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02140775","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":21,"referenced_works":["https://openalex.org/W66060913","https://openalex.org/W749397483","https://openalex.org/W1560787783","https://openalex.org/W1590879322","https://openalex.org/W1976066180","https://openalex.org/W1980357388","https://openalex.org/W2002739878","https://openalex.org/W2009767545","https://openalex.org/W2015632604","https://openalex.org/W2018850201","https://openalex.org/W2023799556","https://openalex.org/W2049460408","https://openalex.org/W2050400201","https://openalex.org/W2059586807","https://openalex.org/W2077915982","https://openalex.org/W2083529130","https://openalex.org/W2186590998","https://openalex.org/W2313114995","https://openalex.org/W2486806899","https://openalex.org/W2798909945","https://openalex.org/W3046325486"],"related_works":["https://openalex.org/W2497112068","https://openalex.org/W2478378501","https://openalex.org/W330769287","https://openalex.org/W2379354442","https://openalex.org/W3023978726","https://openalex.org/W4210411381","https://openalex.org/W4237112000","https://openalex.org/W2141145028","https://openalex.org/W2470850800","https://openalex.org/W1601452860"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}