{"id":"https://openalex.org/W2000973124","doi":"https://doi.org/10.1137/s0895479800398468","title":"A Hermitian Lanczos Method for Normal Matrices","display_name":"A Hermitian Lanczos Method for Normal Matrices","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2000973124","doi":"https://doi.org/10.1137/s0895479800398468","mag":"2000973124"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479800398468","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479800398468","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":"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/A5063256502","display_name":"Marko Huhtanen","orcid":"https://orcid.org/0000-0001-7219-5896"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Marko Huhtanen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5063256502"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7302,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.83649357,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"23","issue":"4","first_page":"1092","last_page":"1108"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9922000169754028,"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/hermitian-matrix","display_name":"Hermitian matrix","score":0.8784582614898682},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8157845139503479},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6965182423591614},{"id":"https://openalex.org/keywords/lanczos-resampling","display_name":"Lanczos resampling","score":0.6596488952636719},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.632810115814209},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.5224401354789734},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4577521085739136},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4276154339313507},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4257889688014984},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4177796542644501},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.2552693486213684},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23885157704353333},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.232023686170578},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13095563650131226},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08165320754051208}],"concepts":[{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.8784582614898682},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8157845139503479},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6965182423591614},{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.6596488952636719},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.632810115814209},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.5224401354789734},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4577521085739136},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4276154339313507},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4257889688014984},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4177796542644501},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2552693486213684},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23885157704353333},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.232023686170578},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13095563650131226},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08165320754051208},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479800398468","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479800398468","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1488435683","https://openalex.org/W1539593706","https://openalex.org/W1641159079","https://openalex.org/W1980356908","https://openalex.org/W1982602023","https://openalex.org/W1992793565","https://openalex.org/W2009211347","https://openalex.org/W2044262951","https://openalex.org/W2049644675","https://openalex.org/W2056981580","https://openalex.org/W2073891589","https://openalex.org/W2081532256","https://openalex.org/W2085259167","https://openalex.org/W2086900226","https://openalex.org/W2090253743","https://openalex.org/W2136866714","https://openalex.org/W2137029533","https://openalex.org/W2139875628","https://openalex.org/W2140153041","https://openalex.org/W2155216327","https://openalex.org/W2167452337","https://openalex.org/W2246376430","https://openalex.org/W2568342123","https://openalex.org/W4205624883","https://openalex.org/W4206092473","https://openalex.org/W4301491118"],"related_works":["https://openalex.org/W2361901126","https://openalex.org/W2081990255","https://openalex.org/W110533479","https://openalex.org/W2367027423","https://openalex.org/W2950418232","https://openalex.org/W4248194227","https://openalex.org/W4301683480","https://openalex.org/W2047814828","https://openalex.org/W2889932903","https://openalex.org/W4213072858"],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2,23],"algorithm":[3],"for":[4],"iteratively":[5],"solving":[6],"a":[7,12,56,60,78,135],"linear":[8],"system":[9],"Nx=b,":[10],"with":[11,22,47,134],"normal":[13,34,57],"$N\\in":[14],"\\mathbb{C}^{n":[15],"\\times":[16],"n}$":[17],"and":[18,50,68,73],"$b":[19],"\\in":[20],"\\mathbb{C}^n$,":[21],"optimal":[24],"3-term":[25,136],"recurrence":[26],"by":[27,39],"extending":[28],"the":[29,41,53,69,95,106,109,119,127],"Hermitian":[30,48,64,128],"Lanczos":[31],"method":[32],"to":[33,112,115],"matrices.":[35],"This":[36],"is":[37,59,132],"achieved":[38],"considering":[40],"Toeplitz":[42],"decomposition":[43],"N=H+iK":[44],"of":[45,55,97,99],"N":[46,72],"H":[49,74],"K.":[51],"Generically,":[52],"inverse":[54],"matrix":[58,129],"polynomial":[61],"in":[62],"its":[63],"part.":[65],"Using":[66],"this":[67,125,131],"fact":[70],"that":[71],"commute,":[75],"we":[76],"obtain":[77],"minimization":[79],"problem":[80],"$$\\min_{p_{j-1}\\in":[81],"{\\cal":[82,87],"P}_{j-1}}\\left|\\left|":[83],"Np_{j-1}(H)b-b":[84],"\\right|\\right|=":[85],"\\min_{p_{j-1}\\in":[86],"P}_{j-1}}":[88],"\\left|\\left|":[89],"p_{j-1}(H)Nb-b\\right|\\right|,$$":[90],"where":[91],"${\\cal":[92,122],"P}_{j-1}$":[93],"denotes":[94],"set":[96],"polynomials":[98],"degree":[100],"j-1":[101],"at":[102,105],"most.":[103],"Thus,":[104],"jth":[107],"step,":[108],"best":[110],"approximation":[111],"b":[113],"needs":[114],"be":[116],"found":[117],"from":[118],"Krylov":[120],"subspace":[121],"K}_j(H;Nb)$.":[123],"Since":[124],"involves":[126],"H,":[130],"realizable":[133],"recurrence.":[137]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}