{"id":"https://openalex.org/W2012216665","doi":"https://doi.org/10.1137/s0895479897325748","title":"On GMRES-Equivalent Bounded Operators","display_name":"On GMRES-Equivalent Bounded Operators","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2012216665","doi":"https://doi.org/10.1137/s0895479897325748","mag":"2012216665"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479897325748","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479897325748","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/A5031659683","display_name":"Leonid Knizhnerman","orcid":"https://orcid.org/0000-0002-8622-1503"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Leonid Knizhnerman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5031659683"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4655,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6555174,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"22","issue":"1","first_page":"195","last_page":"212"},"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8990800380706787},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.7524285316467285},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7519654035568237},{"id":"https://openalex.org/keywords/bounded-operator","display_name":"Bounded operator","score":0.7026117444038391},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6750723123550415},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5815588235855103},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.580270528793335},{"id":"https://openalex.org/keywords/self-adjoint-operator","display_name":"Self-adjoint operator","score":0.542890727519989},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.5419498682022095},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.5011005401611328},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4559805989265442},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42007607221603394},{"id":"https://openalex.org/keywords/unitary-operator","display_name":"Unitary operator","score":0.4157336950302124},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.4152306616306305},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4126121997833252},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4065285325050354},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3524252772331238},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.331093966960907},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.2220367193222046}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8990800380706787},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.7524285316467285},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7519654035568237},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.7026117444038391},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6750723123550415},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5815588235855103},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.580270528793335},{"id":"https://openalex.org/C171972299","wikidata":"https://www.wikidata.org/wiki/Q6500908","display_name":"Self-adjoint operator","level":3,"score":0.542890727519989},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5419498682022095},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.5011005401611328},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4559805989265442},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42007607221603394},{"id":"https://openalex.org/C188313703","wikidata":"https://www.wikidata.org/wiki/Q1972470","display_name":"Unitary operator","level":3,"score":0.4157336950302124},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.4152306616306305},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4126121997833252},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4065285325050354},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3524252772331238},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.331093966960907},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2220367193222046},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/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},{"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479897325748","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479897325748","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W18468166","https://openalex.org/W101236918","https://openalex.org/W592374772","https://openalex.org/W1539593706","https://openalex.org/W1560263223","https://openalex.org/W1977061454","https://openalex.org/W1984543816","https://openalex.org/W1990182629","https://openalex.org/W2044262951","https://openalex.org/W2060375549","https://openalex.org/W2083033783","https://openalex.org/W2094553393","https://openalex.org/W2140153041","https://openalex.org/W2170009492","https://openalex.org/W3038165843","https://openalex.org/W3038830718"],"related_works":["https://openalex.org/W2042846224","https://openalex.org/W2358905935","https://openalex.org/W2942315554","https://openalex.org/W2804461272","https://openalex.org/W2040391781","https://openalex.org/W3134028852","https://openalex.org/W2375237787","https://openalex.org/W1930195566","https://openalex.org/W4287116713","https://openalex.org/W2164612684"],"abstract_inverted_index":{"Given":[0],"a":[1,7,12,19,86],"bounded":[2,27],"linear":[3],"operator":[4,21,126],"A":[5],"in":[6,88],"Hilbert":[8],"space":[9],"$\\calH$":[10],"and":[11,23,31,35,52,72,93,99],"nonzero":[13],"vector":[14],"$\\mbox{\\eufm":[15],"r}\\in\\calH$,":[16],"we":[17,84],"construct":[18],"unitary":[20],"U":[22,71,92],"(under":[24],"some":[25,111],"conditions)":[26],"self-adjoint":[28],"operators":[29],"P":[30,98],"T":[32],"(nonnegative":[33],"definite":[34],"indefinite,":[36],"respectively)":[37],"such":[38],"that":[39,110],"all":[40],"the":[41,56,60,78,89,94,125,133],"residual":[42],"Krylov":[43],"subspaces":[44],"of":[45,55,80,82,91,97,123],"$(A,\\mbox{\\eufm":[46],"r})$,":[47,49,51],"$(U,\\mbox{\\eufm":[48],"$(P,\\mbox{\\eufm":[50],"$(T,\\mbox{\\eufm":[53],"r})$":[54],"same":[57],"dimension":[58],"for":[59,70,132],"equation":[61],"$Ax=\\mbox{\\eufm":[62],"r}$":[63],"are":[64,104,115,130],"equal.":[65],"When":[66],"possible":[67],"(for":[68],"example,":[69],"P,":[73],"provided":[74],"0":[75],"is":[76,108],"outside":[77],"field":[79],"values":[81],"A),":[83],"estimate":[85],"gap":[87],"spectrum":[90],"condition":[95],"numbers":[96],"T.":[100],"Some":[101],"attainability":[102],"results":[103],"also":[105],"established.":[106],"It":[107],"shown":[109],"analogous":[112],"matrix":[113],"assertions":[114],"valid,":[116],"which":[117],"can":[118],"be":[119],"obtained":[120],"by":[121],"means":[122],"degenerating":[124],"case.":[127,135],"Numerical":[128],"examples":[129],"presented":[131],"finite-dimensional":[134]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}