{"id":"https://openalex.org/W2001767320","doi":"https://doi.org/10.1137/080715159","title":"On Optimal Convergence Rate of the Rational Krylov Subspace Reduction for Electromagnetic Problems in Unbounded Domains","display_name":"On Optimal Convergence Rate of the Rational Krylov Subspace Reduction for Electromagnetic Problems in Unbounded Domains","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2001767320","doi":"https://doi.org/10.1137/080715159","mag":"2001767320"},"language":"en","primary_location":{"id":"doi:10.1137/080715159","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080715159","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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":false,"raw_author_name":"Leonid Knizhnerman","raw_affiliation_strings":["mmd@cge.ru#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"mmd@cge.ru#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111474537","display_name":"Vladimir Druskin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vladimir Druskin","raw_affiliation_strings":["druskin1@slb.com and mzaslavsky@slb.com#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"druskin1@slb.com and mzaslavsky@slb.com#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108483631","display_name":"Mikhail Zaslavsky","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mikhail Zaslavsky","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8582,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.93378265,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"47","issue":"2","first_page":"953","last_page":"971"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9977999925613403,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9977999925613403,"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/T10572","display_name":"Geophysical and Geoelectrical Methods","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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":0.8161603808403015},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.7187703847885132},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6126453280448914},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.5012998580932617},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49604281783103943},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4830835163593292},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4750611484050751},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46754804253578186},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4478614032268524},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4125789403915405},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.16997897624969482},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12353348731994629},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07620599865913391}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8161603808403015},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.7187703847885132},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6126453280448914},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.5012998580932617},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49604281783103943},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4830835163593292},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4750611484050751},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46754804253578186},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4478614032268524},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4125789403915405},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.16997897624969482},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12353348731994629},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07620599865913391},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/080715159","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080715159","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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":25,"referenced_works":["https://openalex.org/W110690611","https://openalex.org/W177010616","https://openalex.org/W592374772","https://openalex.org/W1572758332","https://openalex.org/W1590577697","https://openalex.org/W1591459231","https://openalex.org/W1979084948","https://openalex.org/W1979394450","https://openalex.org/W1984347942","https://openalex.org/W2005904620","https://openalex.org/W2012532168","https://openalex.org/W2032298889","https://openalex.org/W2037589078","https://openalex.org/W2044543226","https://openalex.org/W2054535878","https://openalex.org/W2069970858","https://openalex.org/W2070635738","https://openalex.org/W2079407403","https://openalex.org/W2093433489","https://openalex.org/W2099296901","https://openalex.org/W2126903321","https://openalex.org/W2161344224","https://openalex.org/W2162437887","https://openalex.org/W2316564661","https://openalex.org/W2513236363"],"related_works":["https://openalex.org/W2798286561","https://openalex.org/W3161880765","https://openalex.org/W2323113259","https://openalex.org/W3024740485","https://openalex.org/W3169856766","https://openalex.org/W2897217973","https://openalex.org/W4390722712","https://openalex.org/W2967016861","https://openalex.org/W2047317216","https://openalex.org/W2132719248"],"abstract_inverted_index":{"We":[0,38],"solve":[1],"an":[2,59],"electromagnetic":[3],"frequency":[4,12],"domain":[5],"induction":[6],"problem":[7,41,53],"in":[8,54,82],"$\\mathbf{R}^3$":[9],"for":[10,29,78],"a":[11,30,32],"interval":[13],"using":[14],"rational":[15],"Krylov":[16],"subspace":[17],"(RKS)":[18],"approximation.":[19],"The":[20,71],"RKS":[21],"is":[22,73],"constructed":[23],"by":[24],"spanning":[25],"on":[26],"the":[27,40,43,50,55,66],"solutions":[28],"certain":[31],"priori":[33],"chosen":[34],"set":[35],"of":[36,42,46],"frequencies.":[37],"reduce":[39],"optimal":[44],"choice":[45],"these":[47],"frequencies":[48],"to":[49],"third":[51],"Zolotaryov":[52],"complex":[56],"plane,":[57],"having":[58],"approximate":[60],"closed":[61],"form":[62],"solution,":[63],"and":[64],"determine":[65],"best":[67],"Cauchy\u2013Hadamard":[68],"convergence":[69],"rate.":[70],"theory":[72],"illustrated":[74],"with":[75],"numerical":[76],"examples":[77],"Maxwell's":[79],"equations":[80],"arising":[81],"3D":[83],"magnetotelluric":[84],"geophysical":[85],"exploration.":[86]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}