{"id":"https://openalex.org/W23162187","doi":null,"title":"Rational Approximation of Transfer Functions in the Hyperion Software","display_name":"Rational Approximation of Transfer Functions in the Hyperion Software","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W23162187","mag":"23162187"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.58.8493","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.58.8493","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-sop.inria.fr/apics/hyperion/complexity.pdf","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/inria-00072642v1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113684231","display_name":"Jos\u00e9 Grimm","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jos\u00e9 Grimm","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5113684231"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7667,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.73871332,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"245","last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.6582000255584717,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11236","display_name":"Control Systems and Identification","score":0.6582000255584717,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11081","display_name":"Advanced Control Systems Design","score":0.2786000072956085,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T13487","display_name":"Statistical and numerical algorithms","score":0.017000000923871994,"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/rational-approximation","display_name":"rational approximation","score":0.9129999876022339},{"id":"https://openalex.org/keywords/transfer-function","display_name":"transfer function","score":0.9909999966621399},{"id":"https://openalex.org/keywords/fourier-coefficients","display_name":"Fourier coefficients","score":0.6389999985694885},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.7080000042915344},{"id":"https://openalex.org/keywords/mcmillan-degree","display_name":"McMillan degree","score":0.9089999794960022},{"id":"https://openalex.org/keywords/l-infinity-approximation","display_name":"L-infinity approximation","score":0.75},{"id":"https://openalex.org/keywords/critical-points","display_name":"critical points","score":0.8650000095367432},{"id":"https://openalex.org/keywords/automatic-differentiation","display_name":"automatic differentiation","score":0.9629999995231628},{"id":"https://openalex.org/keywords/numerical-optimization","display_name":"numerical optimization","score":0.628000020980835},{"id":"https://openalex.org/keywords/implementation-complexity","display_name":"implementation complexity","score":0.6840000152587891}],"concepts":[{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.6797571182250977},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.6501337289810181},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.6013002395629883},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.5398567914962769},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.5009043216705322},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4728669822216034},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4638887047767639},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4573812186717987},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4501863420009613},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4438301622867584},{"id":"https://openalex.org/C2776175482","wikidata":"https://www.wikidata.org/wiki/Q1195816","display_name":"Transfer (computing)","level":2,"score":0.44174662232398987},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4377005100250244},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4166802763938904},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40708133578300476},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33532005548477173},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2706853747367859},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0761125385761261},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.58.8493","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.58.8493","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-sop.inria.fr/apics/hyperion/complexity.pdf","raw_type":"text"},{"id":"pmh:hdl:10068/47442","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/47442","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"R - Report"},{"id":"pmh:oai:HAL:inria-00072642v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/inria-00072642v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"[Research Report] RR-4002, INRIA. 2000, pp.245","raw_type":"info:eu-repo/semantics/report"},{"id":"mag:23162187","doi":null,"is_oa":false,"landing_page_url":"https://www-sop.inria.fr/apics/hyperion/complexity.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:HAL:inria-00072642v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/inria-00072642v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"[Research Report] RR-4002, INRIA. 2000, pp.245","raw_type":"info:eu-repo/semantics/report"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1559424279","https://openalex.org/W1572079173","https://openalex.org/W2019230842","https://openalex.org/W2031999868","https://openalex.org/W2032273637","https://openalex.org/W2045937853","https://openalex.org/W2058353891","https://openalex.org/W2977816468"],"related_works":["https://openalex.org/W1574348678","https://openalex.org/W7052273657","https://openalex.org/W2737171474","https://openalex.org/W1954186284","https://openalex.org/W2045937853","https://openalex.org/W1999605182","https://openalex.org/W7033360621","https://openalex.org/W2496373622","https://openalex.org/W7097734453","https://openalex.org/W4283332109"],"abstract_inverted_index":{"The":[0],"objective":[1],"of":[2,44,48,65,86,98],"this":[3],"paper":[4],"is":[5,11,19],"to":[6,54],"explain":[7,29],"how":[8,77],"rational":[9,41],"approximation":[10,50],"performed":[12],"within":[13],"the":[14,25,30,33,52,55,74,90,96,99],"hyperion":[15],"software.":[16],"This":[17,60],"work":[18],"divided":[20],"into":[21],"three":[22],"parts.":[23],"In":[24,89],"first":[26],"part,":[27,92],"we":[28,71,93],"theory":[31],"underlying":[32],"algorithm:":[34],"given":[35],"some":[36],"Fourier":[37,58],"coefficients,":[38],"find":[39],"a":[40,62],"transfer":[42],"function":[43],"McMillan":[45],"degree":[46],"$n$":[47],"best":[49],"in":[51,73],"$l^2$-sense":[53],"correspond-":[56],"ing":[57],"series.":[59],"gives":[61],"certain":[63],"number":[64],"equations":[66],"for":[67],"stationary":[68],"points":[69],"and":[70],"detail":[72],"second":[75],"part":[76],"they":[78],"can":[79],"be":[80],"efficiently":[81],"solved":[82],"numerically,":[83],"using":[84],"techniques":[85],"automatic":[87],"differentiation.":[88],"last":[91],"further":[94],"discuss":[95],"complexity":[97],"implementation":[100],"thus":[101],"obtained.":[102]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2016-06-24T00:00:00"}