{"id":"https://openalex.org/W1595778553","doi":"https://doi.org/10.23919/ecc.2009.7074504","title":"A geometric solution to the cheap spectral factorization problem","display_name":"A geometric solution to the cheap spectral factorization problem","publication_year":2009,"publication_date":"2009-08-01","ids":{"openalex":"https://openalex.org/W1595778553","doi":"https://doi.org/10.23919/ecc.2009.7074504","mag":"1595778553"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2009.7074504","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2009.7074504","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5025973614","display_name":"G. Marro","orcid":null},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giovanni Marro","raw_affiliation_strings":["Dipartimento di Elettronica Informatica e Sistemistica, Universit\u00e0 di Bologna, Bologna, Italy","Dipartimento di Elettronica Informatica e Sistemistica, Universit\u00e0 di Bologna, Viale Risorgimento, 2 - 40136, ITALY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica Informatica e Sistemistica, Universit\u00e0 di Bologna, Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]},{"raw_affiliation_string":"Dipartimento di Elettronica Informatica e Sistemistica, Universit\u00e0 di Bologna, Viale Risorgimento, 2 - 40136, ITALY","institution_ids":["https://openalex.org/I9360294"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026787189","display_name":"Fabio Morbidi","orcid":"https://orcid.org/0000-0002-7187-3410"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Fabio Morbidi","raw_affiliation_strings":["Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Siena, Siena, Italy","Dipartimento di Ingegneria dell\u00bfInformazione, Universit\u00e0 di Siena, Via Roma 56, 53100,Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Siena, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]},{"raw_affiliation_string":"Dipartimento di Ingegneria dell\u00bfInformazione, Universit\u00e0 di Siena, Via Roma 56, 53100,Italy","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056137946","display_name":"Domenico Prattichizzo","orcid":"https://orcid.org/0000-0001-9051-9698"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Domenico Prattichizzo","raw_affiliation_strings":["Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Siena, Siena, Italy","Dipartimento di Ingegneria dell\u00bfInformazione, Universit\u00e0 di Siena, Via Roma 56, 53100,Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Siena, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]},{"raw_affiliation_string":"Dipartimento di Ingegneria dell\u00bfInformazione, Universit\u00e0 di Siena, Via Roma 56, 53100,Italy","institution_ids":["https://openalex.org/I102064193"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"814","last_page":"819"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9896000027656555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.7832548022270203},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5391926765441895},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5188952088356018},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4352192282676697},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4204727113246918},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3953418731689453},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37544235587120056},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3382715880870819},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3367235064506531},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3348035216331482},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3018745183944702},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14319834113121033}],"concepts":[{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.7832548022270203},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5391926765441895},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5188952088356018},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4352192282676697},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4204727113246918},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3953418731689453},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37544235587120056},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3382715880870819},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3367235064506531},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3348035216331482},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3018745183944702},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14319834113121033}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.23919/ecc.2009.7074504","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2009.7074504","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 European Control Conference (ECC)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.741.4552","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.741.4552","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dii.unisi.it/%7Emorbidi/Eng/documenti/articoli/MaMoPr_ECC09.pdf","raw_type":"text"},{"id":"pmh:oai:cris.unibo.it:11585/83662","is_oa":false,"landing_page_url":"http://hdl.handle.net/11585/83662","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:usiena-air.unisi.it:11365/5001","is_oa":false,"landing_page_url":"http://hdl.handle.net/11365/5001","pdf_url":null,"source":{"id":"https://openalex.org/S4377196319","display_name":"Use Siena air (University of Siena)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102064193","host_organization_name":"University of Siena","host_organization_lineage":["https://openalex.org/I102064193"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1507624518","https://openalex.org/W1556970733","https://openalex.org/W1595932937","https://openalex.org/W1601183739","https://openalex.org/W1995590150","https://openalex.org/W2020947748","https://openalex.org/W2023723226","https://openalex.org/W2023874179","https://openalex.org/W2028343597","https://openalex.org/W2042555365","https://openalex.org/W2050185337","https://openalex.org/W2056516560","https://openalex.org/W2118589723","https://openalex.org/W2125299152","https://openalex.org/W2132658950","https://openalex.org/W2142420395","https://openalex.org/W2158663867","https://openalex.org/W2163101083","https://openalex.org/W2171352244","https://openalex.org/W2186488025","https://openalex.org/W2294489281","https://openalex.org/W2339524658","https://openalex.org/W2858650168"],"related_works":["https://openalex.org/W587735977","https://openalex.org/W1978142926","https://openalex.org/W3157395178","https://openalex.org/W2794559785","https://openalex.org/W2028768252","https://openalex.org/W2371558776","https://openalex.org/W2045569473","https://openalex.org/W2364426643","https://openalex.org/W2022216752","https://openalex.org/W2399388599"],"abstract_inverted_index":{"The":[0],"paper":[1],"studies":[2],"the":[3,9,22,26,33,36,45,56,60,63],"cheap":[4],"spectral":[5,46],"factorization":[6,47],"problem":[7],"in":[8],"state":[10],"space":[11],"from":[12],"a":[13],"strictly":[14],"geometric":[15,23],"viewpoint.":[16],"A":[17,52],"new":[18],"solution":[19],"based":[20],"on":[21],"properties":[24],"of":[25,62],"related":[27],"Hamiltonian":[28],"system":[29],"is":[30,49],"proposed":[31,64],"and":[32,44,58],"connection":[34],"between":[35],"H":[37],"<sub":[38],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[39],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[40],"-optimal":[41],"model":[42],"following":[43],"problems":[48],"pointed":[50],"out.":[51],"numerical":[53],"example":[54],"illustrates":[55],"theory":[57],"shows":[59],"effectiveness":[61],"solution.":[65]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
