{"id":"https://openalex.org/W2031839014","doi":"https://doi.org/10.1137/08072454x","title":"The Iterative Solver RISOLV with Application to the Exterior Helmholtz Problem","display_name":"The Iterative Solver RISOLV with Application to the Exterior Helmholtz Problem","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2031839014","doi":"https://doi.org/10.1137/08072454x","mag":"2031839014"},"language":"en","primary_location":{"id":"doi:10.1137/08072454x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/08072454x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5018017081","display_name":"Hillel Tal\u2010Ezer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hillel Tal-Ezer","raw_affiliation_strings":["hillel@mta.ac.il#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"hillel@mta.ac.il#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011112251","display_name":"Eli Turkel","orcid":"https://orcid.org/0000-0003-4273-0303"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eli Turkel","raw_affiliation_strings":["turkel@post.tau.ac.il#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"turkel@post.tau.ac.il#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6871,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70996487,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"32","issue":"1","first_page":"463","last_page":"475"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9993000030517578,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9965999722480774,"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/mathematics","display_name":"Mathematics","score":0.7944765090942383},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.7471296191215515},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5602108240127563},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5130850076675415},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.5041526556015015},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4004899263381958},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3910824954509735},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38221439719200134},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35414838790893555},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.1828450858592987}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7944765090942383},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7471296191215515},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5602108240127563},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5130850076675415},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.5041526556015015},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4004899263381958},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3910824954509735},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38221439719200134},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35414838790893555},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.1828450858592987},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/08072454x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/08072454x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6000000238418579,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W140916375","https://openalex.org/W1506342804","https://openalex.org/W1523113578","https://openalex.org/W1537020201","https://openalex.org/W1985014527","https://openalex.org/W1990351032","https://openalex.org/W1997245285","https://openalex.org/W2003894508","https://openalex.org/W2006651457","https://openalex.org/W2017959572","https://openalex.org/W2018850201","https://openalex.org/W2022819055","https://openalex.org/W2023488486","https://openalex.org/W2039393767","https://openalex.org/W2040298674","https://openalex.org/W2048269627","https://openalex.org/W2048981224","https://openalex.org/W2069595221","https://openalex.org/W2075962499","https://openalex.org/W2078027443","https://openalex.org/W2080114591","https://openalex.org/W2082971559","https://openalex.org/W2085259167","https://openalex.org/W2095572167","https://openalex.org/W2117949169","https://openalex.org/W2130552965","https://openalex.org/W2139077927","https://openalex.org/W2140153041","https://openalex.org/W2142094322","https://openalex.org/W2155216327","https://openalex.org/W2157099554","https://openalex.org/W2316564661","https://openalex.org/W2488648946"],"related_works":["https://openalex.org/W2092805352","https://openalex.org/W4310647160","https://openalex.org/W2138940359","https://openalex.org/W3132719053","https://openalex.org/W2970228285","https://openalex.org/W2313389934","https://openalex.org/W2127047223","https://openalex.org/W2264624547","https://openalex.org/W4200634329","https://openalex.org/W2800124757"],"abstract_inverted_index":{"The":[0,36,101,129,194],"innermost":[1],"computational":[2,30],"kernel":[3],"of":[4,14,17,27,74,98,113,169,172,192,210],"many":[5],"large-scale":[6,80],"scientific":[7],"applications":[8],"is":[9,43,50,103,109,147,166,180,197],"often":[10,51],"a":[11,24,71,122,133,181,208,231],"large":[12,232],"set":[13,168,209],"linear":[15,144,211],"equations":[16],"the":[18,28,34,88,96,107,155,167,184,190,203,215,224],"form":[19],"$Ax=b$":[20],"which":[21,159,175,187,213,228],"typically":[22],"consumes":[23],"significant":[25],"portion":[26],"overall":[29],"time":[31],"required":[32],"by":[33],"simulation.":[35],"traditional":[37],"approach":[38,49],"for":[39,62,126,151],"solving":[40,141],"this":[41],"problem":[42],"to":[44,118,120,154,230],"use":[45],"direct":[46,56,67,99],"methods.":[47,100],"This":[48],"preferred":[52],"in":[53,79,183,202],"industry":[54],"because":[55],"solvers":[57],"are":[58,87],"robust":[59,123,135],"and":[60,76,136,178,235],"effective":[61],"moderate":[63],"size":[64],"problems.":[65],"However,":[66],"methods":[68,94],"can":[69],"consume":[70],"huge":[72],"amount":[73],"memory,":[75],"CPU":[77],"time,":[78],"cases.":[81],"In":[82],"these":[83],"cases,":[84],"iterative":[85,93,124],"techniques":[86],"only":[89],"viable":[90],"alternative.":[91],"Unfortunately,":[92],"lack":[95],"robustness":[97],"situation":[102],"especially":[104,201],"difficult":[105],"when":[106],"matrix":[108,217],"nonsymmetric.":[110],"A":[111],"lot":[112],"research":[114],"has":[115],"been":[116],"devoted":[117],"trying":[119],"develop":[121],"algorithm":[125,138,196],"nonsymmetric":[127,143],"systems.":[128,145],"present":[130,220],"paper":[131],"describes":[132],"new":[134],"efficient":[137,199],"aimed":[139],"at":[140],"iteratively":[142],"It":[146],"based":[148],"on":[149],"looking":[150],"an":[152,198],"approximation":[153],"\u201coptimal\u201d":[156],"polynomial":[157],"$P_m(z)$":[158],"satisfies":[160,176],"$||P_m(z)||_{\\infty}=\\min_{Q\\in\\Pi_m}||Q(z)||_{\\infty}$,":[161],"$z\\in":[162],"D$,":[163],"where":[164,205],"$\\Pi_m$":[165],"all":[170,189],"polynomials":[171],"degree":[173],"m":[174],"$Q_m(0)=1$":[177],"D":[179],"domain":[182],"complex":[185,236],"plane":[186],"includes":[188],"eigenvalues":[191],"A.":[193,218],"resulting":[195],"one,":[200],"case":[204],"we":[206],"have":[207],"systems":[212],"share":[214],"same":[216],"We":[219],"several":[221],"applications,":[222],"including":[223],"exterior":[225],"Helmholtz":[226],"problem,":[227],"leads":[229],"indefinite,":[233],"nonsymmetric,":[234],"system.":[237]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
