{"id":"https://openalex.org/W2012914863","doi":"https://doi.org/10.1080/00207160701253836","title":"Model-order reduction of large-scale second-order MIMO dynamical systems via a block second-order Arnoldi method","display_name":"Model-order reduction of large-scale second-order MIMO dynamical systems via a block second-order Arnoldi method","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2012914863","doi":"https://doi.org/10.1080/00207160701253836","mag":"2012914863"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701253836","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701253836","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5053003412","display_name":"Yiqin Lin","orcid":"https://orcid.org/0000-0003-2813-3860"},"institutions":[{"id":"https://openalex.org/I24407930","display_name":"Hunan University of Science and Engineering","ror":"https://ror.org/04ymz0q33","country_code":"CN","type":"education","lineage":["https://openalex.org/I24407930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yiqin Lin","raw_affiliation_strings":["a Department of Mathematics and Computational Science , Hunan University of Science and Engineering , Yongzhou, 425100, P.R. China","Department of Mathematics and Computational Science , Hunan University of Science and Engineering , Yongzhou, 425100, P.R. China"],"affiliations":[{"raw_affiliation_string":"a Department of Mathematics and Computational Science , Hunan University of Science and Engineering , Yongzhou, 425100, P.R. China","institution_ids":["https://openalex.org/I24407930"]},{"raw_affiliation_string":"Department of Mathematics and Computational Science , Hunan University of Science and Engineering , Yongzhou, 425100, P.R. China","institution_ids":["https://openalex.org/I24407930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018729096","display_name":"Liang Bao","orcid":"https://orcid.org/0000-0003-1710-4335"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liang Bao","raw_affiliation_strings":["b Institute of Mathematics, School of Mathematical Sciences, Fudan University , Shanghai, 200433, P.R. China","Institute of Mathematics, School of Mathematical Sciences, Fudan University , Shanghai, 200433, P.R. China"],"affiliations":[{"raw_affiliation_string":"b Institute of Mathematics, School of Mathematical Sciences, Fudan University , Shanghai, 200433, P.R. China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Institute of Mathematics, School of Mathematical Sciences, Fudan University , Shanghai, 200433, P.R. China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014988509","display_name":"Yimin Wei","orcid":"https://orcid.org/0000-0001-6192-0546"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yimin Wei","raw_affiliation_strings":["c Ministry of Education , Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University) , P.R. China","Ministry of Education, Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), P.R. China#TAB#"],"affiliations":[{"raw_affiliation_string":"c Ministry of Education , Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University) , P.R. China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Ministry of Education, Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), P.R. China#TAB#","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014988509"],"corresponding_institution_ids":["https://openalex.org/I24943067"],"apc_list":null,"apc_paid":null,"fwci":1.0433,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.75597484,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"84","issue":"7","first_page":"1003","last_page":"1019"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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":0.9998000264167786,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/krylov-subspace","display_name":"Krylov subspace","score":0.8542329668998718},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.7999181747436523},{"id":"https://openalex.org/keywords/model-order-reduction","display_name":"Model order reduction","score":0.7278860807418823},{"id":"https://openalex.org/keywords/arnoldi-iteration","display_name":"Arnoldi iteration","score":0.713074266910553},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.7063271403312683},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7063267230987549},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.6876498460769653},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6072776913642883},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5952064990997314},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5838731527328491},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5529890656471252},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5291602611541748},{"id":"https://openalex.org/keywords/orthographic-projection","display_name":"Orthographic projection","score":0.4940102696418762},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.47171303629875183},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4691428542137146},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.4671788811683655},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4015509784221649},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3480530381202698},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.1721649169921875},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15059223771095276},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.14147740602493286},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07473671436309814},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07084771990776062}],"concepts":[{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.8542329668998718},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.7999181747436523},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.7278860807418823},{"id":"https://openalex.org/C43143463","wikidata":"https://www.wikidata.org/wiki/Q696822","display_name":"Arnoldi iteration","level":4,"score":0.713074266910553},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.7063271403312683},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7063267230987549},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6876498460769653},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6072776913642883},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5952064990997314},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5838731527328491},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5529890656471252},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5291602611541748},{"id":"https://openalex.org/C175694140","wikidata":"https://www.wikidata.org/wiki/Q980329","display_name":"Orthographic projection","level":2,"score":0.4940102696418762},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.47171303629875183},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4691428542137146},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.4671788811683655},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4015509784221649},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3480530381202698},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.1721649169921875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15059223771095276},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.14147740602493286},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07473671436309814},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07084771990776062},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160701253836","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701253836","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322191","display_name":"Hunan University","ror":"https://ror.org/05htk5m33"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W35420751","https://openalex.org/W95449539","https://openalex.org/W210346111","https://openalex.org/W297328598","https://openalex.org/W391578156","https://openalex.org/W747309577","https://openalex.org/W768595465","https://openalex.org/W1498729261","https://openalex.org/W1525137958","https://openalex.org/W1530042124","https://openalex.org/W1539874772","https://openalex.org/W1551480811","https://openalex.org/W1590943005","https://openalex.org/W1648161269","https://openalex.org/W1868559974","https://openalex.org/W1965315468","https://openalex.org/W1966104103","https://openalex.org/W1967348596","https://openalex.org/W1980689671","https://openalex.org/W2008430533","https://openalex.org/W2009762405","https://openalex.org/W2014759801","https://openalex.org/W2034590496","https://openalex.org/W2040293765","https://openalex.org/W2052005273","https://openalex.org/W2065313971","https://openalex.org/W2081996112","https://openalex.org/W2101675953","https://openalex.org/W2103712032","https://openalex.org/W2126903321","https://openalex.org/W2129917554","https://openalex.org/W2151153690","https://openalex.org/W2161344224","https://openalex.org/W2340513506","https://openalex.org/W2501750346","https://openalex.org/W2610857016","https://openalex.org/W2798909945","https://openalex.org/W2946266054","https://openalex.org/W4210405416","https://openalex.org/W4237159693","https://openalex.org/W4285719527","https://openalex.org/W6602499392"],"related_works":["https://openalex.org/W2015942935","https://openalex.org/W3134028852","https://openalex.org/W2037894849","https://openalex.org/W2804908571","https://openalex.org/W2049086028","https://openalex.org/W2468389232","https://openalex.org/W2169765983","https://openalex.org/W2034236710","https://openalex.org/W2058557317","https://openalex.org/W2148733093"],"abstract_inverted_index":{"In":[0],"this":[1,68],"paper,":[2],"we":[3],"present":[4],"a":[5,19,24],"structure-preserving":[6],"model-order":[7],"reduction":[8],"method":[9,21,36],"for":[10],"solving":[11],"large-scale":[12],"second-order":[13,26,33,51],"MIMO":[14],"dynamical":[15],"systems.":[16],"It":[17],"is":[18],"projection":[20,44],"based":[22],"on":[23],"block":[25,32],"Krylov":[27],"subspace.":[28,45],"We":[29],"use":[30],"the":[31,43,50,54,65],"Arnoldi":[34],"(BSOAR)":[35],"to":[37],"generate":[38],"an":[39],"orthonormal":[40],"basis":[41],"of":[42,53,67],"The":[46],"reduced":[47],"system":[48],"preserves":[49],"structure":[52],"original":[55],"system.":[56],"Some":[57],"theoretical":[58],"results":[59],"are":[60],"given.":[61],"Numerical":[62],"experiments":[63],"report":[64],"effectiveness":[66],"method.":[69]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}