{"id":"https://openalex.org/W2002905417","doi":"https://doi.org/10.1007/s00211-011-0370-7","title":"Palindromic quadratization and structure-preserving algorithm for palindromic matrix polynomials of even degree","display_name":"Palindromic quadratization and structure-preserving algorithm for palindromic matrix polynomials of even degree","publication_year":2011,"publication_date":"2011-03-08","ids":{"openalex":"https://openalex.org/W2002905417","doi":"https://doi.org/10.1007/s00211-011-0370-7","mag":"2002905417"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-011-0370-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-011-0370-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","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/A5034443841","display_name":"Tsung\u2010Ming Huang","orcid":"https://orcid.org/0000-0002-2505-2750"},"institutions":[{"id":"https://openalex.org/I134161618","display_name":"National Taiwan Normal University","ror":"https://ror.org/059dkdx38","country_code":"TW","type":"education","lineage":["https://openalex.org/I134161618"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Tsung-Ming Huang","raw_affiliation_strings":["Department of Mathematics, National Taiwan Normal University, Taipei, 116, Taiwan","National Taiwan Normal University, Department of Mathematics, 116, Taipei, Taiwan#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Taiwan Normal University, Taipei, 116, Taiwan","institution_ids":["https://openalex.org/I134161618"]},{"raw_affiliation_string":"National Taiwan Normal University, Department of Mathematics, 116, Taipei, Taiwan#TAB#","institution_ids":["https://openalex.org/I134161618"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101337552","display_name":"Wen\u2010Wei Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Wen-Wei Lin","raw_affiliation_strings":["Department of Mathematics, National Taiwan University, Taipei, 106, Taiwan","National Taiwan University, Department of Mathematics, 106, Taipei, Taiwan#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Taiwan University, Taipei, 106, Taiwan","institution_ids":["https://openalex.org/I16733864"]},{"raw_affiliation_string":"National Taiwan University, Department of Mathematics, 106, Taipei, Taiwan#TAB#","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067718001","display_name":"Wei-Shuo Su","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Wei-Shuo Su","raw_affiliation_strings":["Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 300, Taiwan","National Chiao Tung University, Department of Applied Mathematics, 300, Hsinchu, Taiwan#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 300, Taiwan","institution_ids":["https://openalex.org/I148366613"]},{"raw_affiliation_string":"National Chiao Tung University, Department of Applied Mathematics, 300, Hsinchu, Taiwan#TAB#","institution_ids":["https://openalex.org/I148366613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5034443841"],"corresponding_institution_ids":["https://openalex.org/I134161618"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.6505,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.68906014,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"118","issue":"4","first_page":"713","last_page":"735"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9970999956130981,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9952999949455261,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/palindrome","display_name":"Palindrome","score":0.8285750150680542},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7615383267402649},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7221618890762329},{"id":"https://openalex.org/keywords/matrix-pencil","display_name":"Matrix pencil","score":0.643409788608551},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.511475682258606},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48297181725502014},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.47194212675094604},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4686780571937561},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45602792501449585},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3798619508743286},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3565709590911865},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2042403519153595},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09682592749595642}],"concepts":[{"id":"https://openalex.org/C44667518","wikidata":"https://www.wikidata.org/wiki/Q12321","display_name":"Palindrome","level":4,"score":0.8285750150680542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7615383267402649},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7221618890762329},{"id":"https://openalex.org/C1576492","wikidata":"https://www.wikidata.org/wiki/Q3739929","display_name":"Matrix pencil","level":3,"score":0.643409788608551},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.511475682258606},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48297181725502014},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.47194212675094604},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4686780571937561},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45602792501449585},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3798619508743286},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3565709590911865},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2042403519153595},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09682592749595642},{"id":"https://openalex.org/C98108389","wikidata":"https://www.wikidata.org/wiki/Q412563","display_name":"CRISPR","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00211-011-0370-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-011-0370-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311041","display_name":"National Center for Theoretical Sciences","ror":"https://ror.org/02mfp0b67"},{"id":"https://openalex.org/F4320321040","display_name":"National Science Council","ror":"https://ror.org/02kv4zf79"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W165118365","https://openalex.org/W1493266520","https://openalex.org/W1970606629","https://openalex.org/W1980157955","https://openalex.org/W1988256819","https://openalex.org/W1999834714","https://openalex.org/W2006031755","https://openalex.org/W2022838696","https://openalex.org/W2025090890","https://openalex.org/W2037002891","https://openalex.org/W2044756790","https://openalex.org/W2078570317","https://openalex.org/W2084380046","https://openalex.org/W2092877019","https://openalex.org/W2110442969","https://openalex.org/W2116581037","https://openalex.org/W2117870622","https://openalex.org/W2117948699","https://openalex.org/W2125453344","https://openalex.org/W2157859159","https://openalex.org/W2163336887","https://openalex.org/W2185172447","https://openalex.org/W2608645537","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2056024401","https://openalex.org/W3216258873","https://openalex.org/W2149734642","https://openalex.org/W4311251537","https://openalex.org/W2002905417","https://openalex.org/W2185931218","https://openalex.org/W4320917455","https://openalex.org/W2016290153","https://openalex.org/W2617044949","https://openalex.org/W4205471980"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}