{"id":"https://openalex.org/W2067965928","doi":"https://doi.org/10.1007/s11075-014-9867-3","title":"A numerical study of the Legendre-Galerkin method for the evaluation of the prolate spheroidal wave functions","display_name":"A numerical study of the Legendre-Galerkin method for the evaluation of the prolate spheroidal wave functions","publication_year":2014,"publication_date":"2014-05-04","ids":{"openalex":"https://openalex.org/W2067965928","doi":"https://doi.org/10.1007/s11075-014-9867-3","mag":"2067965928"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-014-9867-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-014-9867-3","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/A5029643166","display_name":"Sebastian Schmutzhard","orcid":"https://orcid.org/0000-0003-1116-6447"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Sebastian Schmutzhard","raw_affiliation_strings":["Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria","Department of Mathematics, University of Vienna, Wien, Austria 1090#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Department of Mathematics, University of Vienna, Wien, Austria 1090#TAB#","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050615613","display_name":"Tomasz Hrycak","orcid":"https://orcid.org/0000-0003-4352-830X"},"institutions":[{"id":"https://openalex.org/I2800119247","display_name":"Acoustics Research Institute","ror":"https://ror.org/04jd9ff79","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I2800119247"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Tomasz Hrycak","raw_affiliation_strings":["Acoustics Research Institute, Wohllebengasse 12-14, 1040, Wien, Austria","Acoustics Research Institute, Wien, Austria 1040#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Acoustics Research Institute, Wohllebengasse 12-14, 1040, Wien, Austria","institution_ids":["https://openalex.org/I2800119247"]},{"raw_affiliation_string":"Acoustics Research Institute, Wien, Austria 1040#TAB#","institution_ids":["https://openalex.org/I2800119247"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016044961","display_name":"Hans G. Feichtinger","orcid":"https://orcid.org/0000-0002-9927-0742"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Hans G. Feichtinger","raw_affiliation_strings":["Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria","Department of Mathematics, University of Vienna, Wien, Austria 1090#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Department of Mathematics, University of Vienna, Wien, Austria 1090#TAB#","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029643166"],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":1.2068,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.76639895,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"68","issue":"4","first_page":"691","last_page":"710"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9959999918937683,"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/T10514","display_name":"Numerical methods in engineering","score":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.8851492404937744},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7885260581970215},{"id":"https://openalex.org/keywords/legendre-function","display_name":"Legendre function","score":0.6960388422012329},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6596119999885559},{"id":"https://openalex.org/keywords/prolate-spheroid","display_name":"Prolate spheroid","score":0.6294665932655334},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.6097975969314575},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5679040551185608},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.5555692315101624},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5545197129249573},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46274736523628235},{"id":"https://openalex.org/keywords/associated-legendre-polynomials","display_name":"Associated Legendre polynomials","score":0.46228885650634766},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4467132091522217},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2522556185722351},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.154756098985672},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11809483170509338},{"id":"https://openalex.org/keywords/gegenbauer-polynomials","display_name":"Gegenbauer polynomials","score":0.09672793745994568},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.0603850781917572}],"concepts":[{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.8851492404937744},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7885260581970215},{"id":"https://openalex.org/C153262748","wikidata":"https://www.wikidata.org/wiki/Q17098449","display_name":"Legendre function","level":3,"score":0.6960388422012329},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6596119999885559},{"id":"https://openalex.org/C197807790","wikidata":"https://www.wikidata.org/wiki/Q208395","display_name":"Prolate spheroid","level":2,"score":0.6294665932655334},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.6097975969314575},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5679040551185608},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.5555692315101624},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5545197129249573},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46274736523628235},{"id":"https://openalex.org/C36956377","wikidata":"https://www.wikidata.org/wiki/Q228376","display_name":"Associated Legendre polynomials","level":5,"score":0.46228885650634766},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4467132091522217},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2522556185722351},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.154756098985672},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11809483170509338},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.09672793745994568},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.0603850781917572},{"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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"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/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-014-9867-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-014-9867-3","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":36,"referenced_works":["https://openalex.org/W580571344","https://openalex.org/W593926650","https://openalex.org/W1563653928","https://openalex.org/W1576347883","https://openalex.org/W1805381866","https://openalex.org/W1967031254","https://openalex.org/W1973312654","https://openalex.org/W1995816184","https://openalex.org/W2006025109","https://openalex.org/W2017456381","https://openalex.org/W2017465632","https://openalex.org/W2021953266","https://openalex.org/W2023583513","https://openalex.org/W2035299799","https://openalex.org/W2067111814","https://openalex.org/W2072396164","https://openalex.org/W2074518966","https://openalex.org/W2086809421","https://openalex.org/W2088801740","https://openalex.org/W2093908016","https://openalex.org/W2109624367","https://openalex.org/W2120062331","https://openalex.org/W2313443574","https://openalex.org/W2480854438","https://openalex.org/W2503127310","https://openalex.org/W2801179766","https://openalex.org/W2963132355","https://openalex.org/W2963600276","https://openalex.org/W2995924920","https://openalex.org/W3103534804","https://openalex.org/W3103598160","https://openalex.org/W3112961938","https://openalex.org/W4237994936","https://openalex.org/W4240906956","https://openalex.org/W4241229523","https://openalex.org/W4320800818"],"related_works":["https://openalex.org/W1607269076","https://openalex.org/W3130427480","https://openalex.org/W2953361964","https://openalex.org/W2053826141","https://openalex.org/W1988418937","https://openalex.org/W2015172806","https://openalex.org/W2505598524","https://openalex.org/W1974031583","https://openalex.org/W2025296287","https://openalex.org/W2112218901"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
