{"id":"https://openalex.org/W2091542044","doi":"https://doi.org/10.1137/060651859","title":"Numerical Methods for Computing Nonlinear Eigenpairs: Part I. Iso-Homogeneous Cases","display_name":"Numerical Methods for Computing Nonlinear Eigenpairs: Part I. Iso-Homogeneous Cases","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2091542044","doi":"https://doi.org/10.1137/060651859","mag":"2091542044"},"language":"en","primary_location":{"id":"doi:10.1137/060651859","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060651859","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/A5102707684","display_name":"Xudong Yao","orcid":"https://orcid.org/0000-0002-4862-263X"},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xudong Yao","raw_affiliation_strings":["Department of Mathematics, University of Connecticut, Storrs, CT 06269"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Connecticut, Storrs, CT 06269","institution_ids":["https://openalex.org/I140172145"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017633979","display_name":"Jianxin Zhou","orcid":"https://orcid.org/0000-0003-2111-2127"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jianxin Zhou","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, TX 77843"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, TX 77843","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102707684"],"corresponding_institution_ids":["https://openalex.org/I140172145"],"apc_list":null,"apc_paid":null,"fwci":2.0771,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.86827773,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"29","issue":"4","first_page":"1355","last_page":"1374"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9988999962806702,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.998199999332428,"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/mathematics","display_name":"Mathematics","score":0.7545393109321594},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5305455327033997},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5098339915275574},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4680585265159607},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4502158761024475},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.4456713795661926},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.4448707103729248},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.4153844118118286},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33674395084381104},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.16976645588874817}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7545393109321594},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5305455327033997},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5098339915275574},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4680585265159607},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4502158761024475},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.4456713795661926},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4448707103729248},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.4153844118118286},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33674395084381104},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.16976645588874817},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/060651859","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060651859","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"},{"id":"pmh:oai:oaktrust.library.tamu.edu:1969.1/180692","is_oa":false,"landing_page_url":"https://hdl.handle.net/1969.1/180692","pdf_url":null,"source":{"id":"https://openalex.org/S4306400291","display_name":"OakTrust (Texas A&M University Libraries)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I91045830","host_organization_name":"Texas A&M University","host_organization_lineage":["https://openalex.org/I91045830"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1502485581","https://openalex.org/W1547403762","https://openalex.org/W1965196511","https://openalex.org/W1967676806","https://openalex.org/W1970474373","https://openalex.org/W1973036914","https://openalex.org/W1983078904","https://openalex.org/W1984241241","https://openalex.org/W1984781443","https://openalex.org/W1995464753","https://openalex.org/W1996367569","https://openalex.org/W2003940306","https://openalex.org/W2008310509","https://openalex.org/W2012018158","https://openalex.org/W2012844477","https://openalex.org/W2023444505","https://openalex.org/W2025686400","https://openalex.org/W2025847892","https://openalex.org/W2026106782","https://openalex.org/W2028803634","https://openalex.org/W2029065864","https://openalex.org/W2030004448","https://openalex.org/W2033142362","https://openalex.org/W2036698365","https://openalex.org/W2038991247","https://openalex.org/W2046128078","https://openalex.org/W2049152374","https://openalex.org/W2053640807","https://openalex.org/W2064169085","https://openalex.org/W2065728117","https://openalex.org/W2068205194","https://openalex.org/W2068234100","https://openalex.org/W2071438440","https://openalex.org/W2077204127","https://openalex.org/W2081374615","https://openalex.org/W2083569938","https://openalex.org/W2084105802","https://openalex.org/W2106260664","https://openalex.org/W2161652417","https://openalex.org/W3102111330","https://openalex.org/W3184713643","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4302419125","https://openalex.org/W2766128145","https://openalex.org/W4300623652","https://openalex.org/W121031341","https://openalex.org/W2038878154","https://openalex.org/W2111271529","https://openalex.org/W2464780829","https://openalex.org/W4290982745","https://openalex.org/W2963746646","https://openalex.org/W3217737408"],"abstract_inverted_index":{"With":[0],"a":[1,5,13],"Rayleigh":[2],"quotient":[3],"formulation,":[4],"local":[6],"minimax":[7],"method":[8],"is":[9,32,72],"developed":[10],"to":[11,34,63],"solve":[12],"class":[14],"of":[15,38,68],"(iso-homogeneous)":[16],"nonlinear":[17],"eigenpair":[18],"problems":[19],"for":[20,57],"multiple":[21],"solutions":[22],"in":[23],"Banach":[24],"spaces":[25],"following":[26],"their":[27,46],"instability":[28,66],"order.":[29],"The":[30],"algorithm":[31],"implemented":[33],"compute":[35],"(weighted)":[36],"eigenpairs":[37],"the":[39],"p-Laplacian.":[40],"Numerical":[41],"eigenfunctions":[42],"are":[43,55],"illustrated":[44],"by":[45],"graphics.":[47],"Several":[48],"interesting":[49],"phenomena":[50],"have":[51],"been":[52],"observed":[53],"and":[54,65],"open":[56],"further":[58],"investigation.":[59],"Mathematical":[60],"analysis":[61],"related":[62],"convergence":[64],"order":[67],"computed":[69],"eigenfunctions,":[70],"etc.,":[71],"also":[73],"presented.":[74]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}