{"id":"https://openalex.org/W2778433150","doi":"https://doi.org/10.1137/19m1246213","title":"Extended and Improved Criss-Cross Algorithms for Computing the Spectral Value Set Abscissa and Radius","display_name":"Extended and Improved Criss-Cross Algorithms for Computing the Spectral Value Set Abscissa and Radius","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2778433150","doi":"https://doi.org/10.1137/19m1246213","mag":"2778433150"},"language":"en","primary_location":{"id":"doi:10.1137/19m1246213","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1246213","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1712.10067","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060985095","display_name":"Peter Benner","orcid":"https://orcid.org/0000-0003-3362-4103"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Peter Benner","raw_affiliation_strings":["Max-Planck-Society"],"raw_orcid":"https://orcid.org/0000-0003-3362-4103","affiliations":[{"raw_affiliation_string":"Max-Planck-Society","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025247322","display_name":"Tim Mitchell","orcid":"https://orcid.org/0000-0002-8426-0242"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tim Mitchell","raw_affiliation_strings":["Max-Planck-Society"],"raw_orcid":"https://orcid.org/0000-0002-8426-0242","affiliations":[{"raw_affiliation_string":"Max-Planck-Society","institution_ids":["https://openalex.org/I149899117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0111033,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"40","issue":"4","first_page":"1325","last_page":"1352"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9968000054359436,"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":0.9968000054359436,"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":0.9962999820709229,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6147746443748474},{"id":"https://openalex.org/keywords/ordinate","display_name":"Ordinate","score":0.5890299677848816},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5817331075668335},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5229131579399109},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44253015518188477},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.41347092390060425},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33609139919281006},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2494150996208191},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12597563862800598}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6147746443748474},{"id":"https://openalex.org/C148405484","wikidata":"https://www.wikidata.org/wiki/Q58485726","display_name":"Ordinate","level":2,"score":0.5890299677848816},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5817331075668335},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5229131579399109},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44253015518188477},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.41347092390060425},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33609139919281006},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2494150996208191},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12597563862800598},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/19m1246213","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1246213","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1712.10067","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.10067","pdf_url":"https://arxiv.org/pdf/1712.10067","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:pure.mpg.de:item_2525750","is_oa":true,"landing_page_url":"http://hdl.handle.net/21.11116/0000-0000-2C04-B","pdf_url":"https://hdl.handle.net/21.11116/0000-0005-1FEC-0","source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"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":"SIAM Journal on Matrix Analysis and Applications","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1712.10067","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1712.10067","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:2778433150","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1712.10067","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.10067","pdf_url":"https://arxiv.org/pdf/1712.10067","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2778433150.pdf","grobid_xml":"https://content.openalex.org/works/W2778433150.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W149522324","https://openalex.org/W1621905519","https://openalex.org/W1812003359","https://openalex.org/W1984560319","https://openalex.org/W1998990712","https://openalex.org/W2019354131","https://openalex.org/W2032733248","https://openalex.org/W2038516800","https://openalex.org/W2047917018","https://openalex.org/W2049154285","https://openalex.org/W2069400331","https://openalex.org/W2081212476","https://openalex.org/W2100004457","https://openalex.org/W2114792685","https://openalex.org/W2147779187","https://openalex.org/W2156291021","https://openalex.org/W2167193748","https://openalex.org/W2440120183","https://openalex.org/W2501072491","https://openalex.org/W2963845843"],"related_works":["https://openalex.org/W2979140977","https://openalex.org/W2473578035","https://openalex.org/W2771992339","https://openalex.org/W3009094226","https://openalex.org/W24939243","https://openalex.org/W3104511711","https://openalex.org/W744571450","https://openalex.org/W2952462506","https://openalex.org/W2952783979","https://openalex.org/W3098912714","https://openalex.org/W2187224761","https://openalex.org/W2061228897","https://openalex.org/W2396767758","https://openalex.org/W3040586277","https://openalex.org/W2803473363","https://openalex.org/W3009108566","https://openalex.org/W2151769723","https://openalex.org/W2094435468","https://openalex.org/W2780206593","https://openalex.org/W1569969230"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,31,60],"extend":[4],"the":[5,11,27,34,67,79,90],"original":[6,91],"criss-cross":[7,101],"algorithms":[8,102],"for":[9,26,115],"computing":[10,78],"$\\varepsilon$-pseudospectral":[12],"abscissa":[13],"and":[14,53,112,120],"radius":[15],"to":[16,45,85],"general":[17],"spectral":[18,117],"value":[19,81,118],"sets.":[20],"By":[21],"proposing":[22],"new":[23,63],"root-finding-based":[24],"strategies":[25],"horizontal/radial":[28],"search":[29],"subphases,":[30],"significantly":[32],"reduce":[33],"number":[35],"of":[36,65,89],"expensive":[37],"Hamiltonian":[38],"eigenvalue":[39],"decompositions":[40],"incurred,":[41],"which":[42],"typically":[43],"translates":[44],"meaningful":[46],"speedups":[47],"in":[48],"overall":[49],"computation":[50],"times.":[51],"Furthermore,":[52],"partly":[54],"necessitated":[55],"by":[56],"our":[57,96,99],"root-finding":[58],"approach,":[59],"develop":[61],"a":[62],"way":[64],"handling":[66],"singular":[68],"pencils":[69],"or":[70],"problematic":[71],"interior":[72],"searches":[73],"that":[74,93],"can":[75],"arise":[76],"when":[77],"$\\varepsilon$-spectral":[80],"set":[82,119],"radius.":[83],"Compared":[84],"would-be":[86],"direct":[87],"extensions":[88],"algorithms,":[92],"is,":[94],"without":[95],"additional":[97],"modifications,":[98],"improved":[100],"are":[103],"not":[104],"only":[105],"noticeably":[106],"faster":[107],"but":[108],"also":[109],"more":[110],"robust":[111],"numerically":[113],"accurate,":[114],"both":[116],"pseudospectral":[121],"problems.":[122]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-25T08:15:23.626066","created_date":"2022-10-03T00:00:00"}