{"id":"https://openalex.org/W2045318013","doi":"https://doi.org/10.1007/bf02141741","title":"Componentwise error analysis for FFTs with applications to fast Helmholtz solvers","display_name":"Componentwise error analysis for FFTs with applications to fast Helmholtz solvers","publication_year":1996,"publication_date":"1996-03-01","ids":{"openalex":"https://openalex.org/W2045318013","doi":"https://doi.org/10.1007/bf02141741","mag":"2045318013"},"language":"en","primary_location":{"id":"doi:10.1007/bf02141741","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02141741","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/A5111911025","display_name":"M. Arioli","orcid":null},"institutions":[{"id":"https://openalex.org/I4210129724","display_name":"Istituto di Genetica Molecolare","ror":"https://ror.org/03qpd8w66","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210129724","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"M. Arioli","raw_affiliation_strings":["Istituto di Analisi Numerica, Consiglio Nazionale delle Ricerche, via Abbiategrasso 209, I-27100, Pavia, Italy","Istituto di Analisi Numerica, Consiglio Nazionale delle Ricerche, Pavia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Istituto di Analisi Numerica, Consiglio Nazionale delle Ricerche, via Abbiategrasso 209, I-27100, Pavia, Italy","institution_ids":["https://openalex.org/I4210129724"]},{"raw_affiliation_string":"Istituto di Analisi Numerica, Consiglio Nazionale delle Ricerche, Pavia, Italy","institution_ids":["https://openalex.org/I4210129724"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069525654","display_name":"Hans Munthe\u2013Kaas","orcid":"https://orcid.org/0000-0002-4456-3150"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"H. Munthe-Kaas","raw_affiliation_strings":["Institute for Informatics, University of Bergen, N-5020, Bergen, Norway","Institute for Informatics, University of Bergen, Bergen, Norway#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Informatics, University of Bergen, N-5020, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Institute for Informatics, University of Bergen, Bergen, Norway#TAB#","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004435511","display_name":"Lorenzo Valdettaro","orcid":null},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"L. Valdettaro","raw_affiliation_strings":["Dipartimento di Matematica, Politecnico di Milano, piazza Leonardo da Vinci, I-20133, Milano, Italy","Dipartimento di Matematica, Politecnico di Milano, Milano, Italy#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Politecnico di Milano, piazza Leonardo da Vinci, I-20133, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Dipartimento di Matematica, Politecnico di Milano, Milano, Italy#TAB#","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.14305913,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"12","issue":"1","first_page":"65","last_page":"88"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9965000152587891,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/mathematics","display_name":"Mathematics","score":0.7711577415466309},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.7063107490539551},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.6454195976257324},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.6106740832328796},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5784967541694641},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.561781644821167},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5299903750419617},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4573667645454407},{"id":"https://openalex.org/keywords/machine-epsilon","display_name":"Machine epsilon","score":0.44827768206596375},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4439285695552826},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44233840703964233},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.43424224853515625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2571585178375244},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15984869003295898},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11252057552337646}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7711577415466309},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.7063107490539551},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.6454195976257324},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.6106740832328796},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5784967541694641},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.561781644821167},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5299903750419617},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4573667645454407},{"id":"https://openalex.org/C203739276","wikidata":"https://www.wikidata.org/wiki/Q1780355","display_name":"Machine epsilon","level":2,"score":0.44827768206596375},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4439285695552826},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44233840703964233},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.43424224853515625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2571585178375244},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15984869003295898},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11252057552337646},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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":2,"locations":[{"id":"doi:10.1007/bf02141741","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02141741","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"},{"id":"pmh:oai:re.public.polimi.it:11311/663616","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/663616","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1549220217","https://openalex.org/W1912930600","https://openalex.org/W1955565642","https://openalex.org/W1969307568","https://openalex.org/W1973374823","https://openalex.org/W2022765508","https://openalex.org/W2050962398","https://openalex.org/W2051150863","https://openalex.org/W2061171222","https://openalex.org/W2069441027","https://openalex.org/W2070025169","https://openalex.org/W2129956165","https://openalex.org/W2131778920","https://openalex.org/W2134572726","https://openalex.org/W2170142399","https://openalex.org/W2408478130","https://openalex.org/W2798497704","https://openalex.org/W4298060601"],"related_works":["https://openalex.org/W3039927303","https://openalex.org/W4226335541","https://openalex.org/W4231731735","https://openalex.org/W180579544","https://openalex.org/W4242955624","https://openalex.org/W2061091230","https://openalex.org/W2097245422","https://openalex.org/W2134876043","https://openalex.org/W2990673076","https://openalex.org/W1496637154"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
