{"id":"https://openalex.org/W4302028453","doi":"https://doi.org/10.1515/cmam-2022-0150","title":"Integral Representations and Quadrature Schemes for the Modified Hilbert Transformation","display_name":"Integral Representations and Quadrature Schemes for the Modified Hilbert Transformation","publication_year":2022,"publication_date":"2022-10-05","ids":{"openalex":"https://openalex.org/W4302028453","doi":"https://doi.org/10.1515/cmam-2022-0150"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2022-0150","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2022-0150","pdf_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2022-0150/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2022-0150/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073774238","display_name":"Marco Zank","orcid":"https://orcid.org/0000-0002-4146-1474"},"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":"Marco Zank","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik , Universit\u00e4t Wien , Oskar-Morgenstern-Platz 1, 1090 Wien , Austria"],"raw_orcid":"https://orcid.org/0000-0002-4146-1474","affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik , Universit\u00e4t Wien , Oskar-Morgenstern-Platz 1, 1090 Wien , Austria","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073774238"],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":null,"apc_paid":null,"fwci":0.9968,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.70521494,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"23","issue":"2","first_page":"473","last_page":"489"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9987000226974487,"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/mathematics","display_name":"Mathematics","score":0.755054235458374},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6731003522872925},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46469730138778687},{"id":"https://openalex.org/keywords/clenshaw\u2013curtis-quadrature","display_name":"Clenshaw\u2013Curtis quadrature","score":0.4605395793914795},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.45322662591934204},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.436518132686615},{"id":"https://openalex.org/keywords/singular-integral","display_name":"Singular integral","score":0.4249700605869293},{"id":"https://openalex.org/keywords/gauss\u2013kronrod-quadrature-formula","display_name":"Gauss\u2013Kronrod quadrature formula","score":0.4130394160747528},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34966132044792175},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.25232017040252686},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.21259436011314392},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.20365428924560547}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.755054235458374},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6731003522872925},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46469730138778687},{"id":"https://openalex.org/C172657837","wikidata":"https://www.wikidata.org/wiki/Q5131618","display_name":"Clenshaw\u2013Curtis quadrature","level":5,"score":0.4605395793914795},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.45322662591934204},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.436518132686615},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.4249700605869293},{"id":"https://openalex.org/C14103991","wikidata":"https://www.wikidata.org/wiki/Q5527852","display_name":"Gauss\u2013Kronrod quadrature formula","level":4,"score":0.4130394160747528},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34966132044792175},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.25232017040252686},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.21259436011314392},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.20365428924560547},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2022-0150","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2022-0150","pdf_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2022-0150/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1515/cmam-2022-0150","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2022-0150","pdf_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2022-0150/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4302028453.pdf","grobid_xml":"https://content.openalex.org/works/W4302028453.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1521778258","https://openalex.org/W2013519714","https://openalex.org/W2084179710","https://openalex.org/W3014898465","https://openalex.org/W3099120560","https://openalex.org/W3135013903","https://openalex.org/W3189682286","https://openalex.org/W4205815276","https://openalex.org/W4210443583","https://openalex.org/W4229840132","https://openalex.org/W4247548326"],"related_works":["https://openalex.org/W4237740072","https://openalex.org/W2079157924","https://openalex.org/W4389939969","https://openalex.org/W1995933053","https://openalex.org/W2620379969","https://openalex.org/W1631331635","https://openalex.org/W2929787118","https://openalex.org/W2050586781","https://openalex.org/W2552202259","https://openalex.org/W2367332464"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"present":[2],"quadrature":[3,63,97,114,119],"schemes":[4,64,120],"to":[5,51,110],"calculate":[6],"matrices":[7,17,50],"where":[8,125],"the":[9,33,40,46,73,84,101,111,117],"so-called":[10],"modified":[11,34,74,85],"Hilbert":[12,35,75,86],"transformation":[13,36,87],"is":[14,37,121,129],"involved.":[15],"These":[16],"occur":[18],"as":[19],"temporal":[20],"parts":[21],"of":[22,27,48,72,83,113],"Galerkin":[23],"finite":[24],"element":[25],"discretizations":[26],"parabolic":[28],"or":[29],"hyperbolic":[30],"problems":[31],"when":[32],"used":[38],"for":[39,54,116],"variational":[41],"setting.":[42],"This":[43],"work":[44],"provides":[45],"calculation":[47],"these":[49,78,92],"machine":[52],"precision":[53],"arbitrary":[55],"polynomial":[56],"degrees":[57],"and":[58],"non-uniform":[59],"meshes.":[60],"The":[61],"proposed":[62,118],"are":[65,88],"based":[66],"on":[67],"weakly":[68,79],"singular":[69,80],"integral":[70,81,93],"representations":[71,82],"transformation.":[76],"First,":[77],"proven.":[89],"Second,":[90],"using":[91],"representations,":[94],"we":[95],"derive":[96],"schemes,":[98],"which":[99],"treat":[100],"occurring":[102],"singularities":[103],"appropriately.":[104],"Thus,":[105],"exponential":[106,127],"convergence":[107,128],"with":[108],"respect":[109],"number":[112],"nodes":[115],"achieved.":[122],"Numerical":[123],"results,":[124],"this":[126,132],"observed,":[130],"conclude":[131],"work.":[133]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
