{"id":"https://openalex.org/W7221785380","doi":"https://doi.org/10.48550/arxiv.2610.16249","title":"$H_2$-optimal model order reduction using hyperbolic geometry","display_name":"$H_2$-optimal model order reduction using hyperbolic geometry","publication_year":2026,"publication_date":"2026-10-12","ids":{"openalex":"https://openalex.org/W7221785380","doi":"https://doi.org/10.48550/arxiv.2610.16249"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.16249","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16249","pdf_url":"https://arxiv.org/pdf/2610.16249","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.16249","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107289610","display_name":"Andrea Angino","orcid":"https://orcid.org/0009-0000-8525-375X","observed_orcids":["https://orcid.org/0009-0000-8525-375X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Angino, Andrea","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090505237","display_name":"Tam\u00e1s D\u00f3zsa","orcid":"https://orcid.org/0000-0003-0919-4385","observed_orcids":["https://orcid.org/0000-0003-0919-4385"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D\u00f3zsa, Tam\u00e1s","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5103056883","display_name":"Matthias Voigt","orcid":"https://orcid.org/0000-0001-8491-1861","observed_orcids":["https://orcid.org/0000-0001-8491-1861"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Voigt, Matthias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.8095999956130981,"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":0.8095999956130981,"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/T11081","display_name":"Advanced Control Systems Design","score":0.1639000028371811,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.006200000178068876,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/model-reduction","display_name":"model reduction","score":0.6930000185966492},{"id":"https://openalex.org/keywords/linear-time-invariant-systems","display_name":"linear time-invariant systems","score":0.8360000252723694},{"id":"https://openalex.org/keywords/stability-of-reduced-models","display_name":"stability of reduced models","score":0.628000020980835},{"id":"https://openalex.org/keywords/hyperbolic-geometry","display_name":"hyperbolic geometry","score":0.9419999718666077},{"id":"https://openalex.org/keywords/poincare-disk","display_name":"Poincar\u00e9 disk","score":0.8840000033378601},{"id":"https://openalex.org/keywords/newton-type-methods","display_name":"Newton-type methods","score":0.6970000267028809},{"id":"https://openalex.org/keywords/hyperbolic-geodesics","display_name":"hyperbolic geodesics","score":0.8920000195503235},{"id":"https://openalex.org/keywords/equilibrium-function","display_name":"equilibrium function","score":0.8270000219345093},{"id":"https://openalex.org/keywords/siso-systems","display_name":"SISO systems","score":0.7929999828338623}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6852999925613403},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5756000280380249},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5637000203132629},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49559998512268066},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.45339998602867126},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.4447000026702881},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4083999991416931},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.3968000113964081},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.3917999863624573},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.3840999901294708},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.3727000057697296},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.365200012922287},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.35249999165534973},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.33730000257492065},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.3361000120639801},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3343999981880188},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.32989999651908875},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.32019999623298645},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.3091999888420105},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30090001225471497},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.2935999929904938},{"id":"https://openalex.org/C50429861","wikidata":"https://www.wikidata.org/wiki/Q3554830","display_name":"Stable manifold","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2782999873161316},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2696000039577484},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C194777461","wikidata":"https://www.wikidata.org/wiki/Q1085860","display_name":"Root-finding algorithm","level":3,"score":0.2567000091075897},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.2547000050544739},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.16249","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16249","pdf_url":"https://arxiv.org/pdf/2610.16249","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2610.16249","doi":"https://doi.org/10.48550/arxiv.2610.16249","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.16249","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.16249","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16249","pdf_url":"https://arxiv.org/pdf/2610.16249","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221785380.pdf","grobid_xml":"https://content.openalex.org/works/W7221785380.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7066070728","https://openalex.org/W2071755436","https://openalex.org/W7098542389","https://openalex.org/W6926067209","https://openalex.org/W2118995214","https://openalex.org/W3135240482","https://openalex.org/W2771232379","https://openalex.org/W7140956419","https://openalex.org/W2118958734","https://openalex.org/W2902676923"],"abstract_inverted_index":{"We":[0,75,95,151],"revisit":[1],"the":[2,29,38,41,73,81,98,109,128,143,175,181],"problem":[3,119],"of":[4,40,64,72,100,111,130],"approximating":[5],"a":[6,12,53,123],"linear":[7],"time-invariant":[8],"LTI":[9,67,163],"model":[10,14],"by":[11,108],"reduced-order":[13],"(ROM)":[15],"in":[16,36,80],"an":[17,92,101],"$H_2$-optimal":[18,62,102],"sense.":[19],"A":[20],"widely":[21],"used":[22,59],"method":[23,125,177],"for":[24,158],"computing":[25],"such":[26],"ROMs":[27],"is":[28,44,120,146],"iterative":[30],"rational":[31],"Krylov":[32],"algorithm":[33],"(IRKA).":[34],"However,":[35],"practice,":[37],"stability":[39,71,144,179],"resulting":[42,116],"ROM":[43,103],"not":[45],"generally":[46],"guaranteed.":[47],"In":[48],"this":[49,112],"work,":[50],"we":[51],"develop":[52,91],"novel":[54],"framework":[55],"that":[56,97,142],"can":[57],"be":[58],"to":[60,87,90],"obtain":[61],"models":[63,173],"single-input":[65],"single-output":[66],"systems":[68,157],"while":[69,174],"enforcing":[70],"ROM.":[74],"use":[76],"Malmquist-Takenaka":[77],"orthogonal":[78],"expansions":[79],"corresponding":[82],"$H_2$-spaces":[83],"and":[84,161],"their":[85],"connection":[86],"hyperbolic":[88,139],"geometry":[89],"equilibrium":[93,113],"function.":[94,114],"show":[96],"poles":[99],"transfer":[104],"function":[105],"are":[106,136],"defined":[107],"zeros":[110],"The":[115],"nonlinear":[117],"root-finding":[118],"solved":[121],"using":[122],"Newton-type":[124],"formulated":[126],"on":[127,155],"products":[129],"Poincar\u00e9":[131],"disk":[132],"manifolds,":[133],"where":[134,168],"updates":[135],"performed":[137],"along":[138],"geodesics":[140],"ensuring":[141],"constraint":[145],"satisfied":[147],"at":[148],"every":[149],"iteration.":[150,182],"present":[152],"numerical":[153],"experiments":[154],"benchmark":[156],"both":[159],"discrete-":[160],"continuous-time":[162],"MOR":[164],"problems,":[165],"including":[166],"examples":[167],"IRKA":[169],"produces":[170],"unstable":[171],"reduced":[172],"proposed":[176],"preserves":[178],"throughout":[180]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-15T00:00:00"}