{"id":"https://openalex.org/W2114817572","doi":"https://doi.org/10.1090/mcom/2990","title":"Existence of \u210b-matrix approximants to the inverses of BEM matrices: The simple-layer operator","display_name":"Existence of \u210b-matrix approximants to the inverses of BEM matrices: The simple-layer operator","publication_year":2015,"publication_date":"2015-06-18","ids":{"openalex":"https://openalex.org/W2114817572","doi":"https://doi.org/10.1090/mcom/2990","mag":"2114817572"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/2990","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/2990","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1311.5028","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019645947","display_name":"Markus Faustmann","orcid":null},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Markus Faustmann","raw_affiliation_strings":["Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstra\u00c3\u009fe 8-10, 1040 Wien, Austria","Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstra\u00dfe 8-10, 1040 Wien, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstra\u00c3\u009fe 8-10, 1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstra\u00dfe 8-10, 1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058356670","display_name":"Jens Markus Melenk","orcid":"https://orcid.org/0000-0001-9024-6028"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Jens Melenk","raw_affiliation_strings":["Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstra\u00c3\u009fe 8-10, 1040 Wien, Austria","Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstra\u00dfe 8-10, 1040 Wien, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstra\u00c3\u009fe 8-10, 1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstra\u00dfe 8-10, 1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022125095","display_name":"Dirk Praetorius","orcid":"https://orcid.org/0000-0002-1977-9830"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Dirk Praetorius","raw_affiliation_strings":["Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstra\u00c3\u009fe 8-10, 1040 Wien, Austria","Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstra\u00dfe 8-10, 1040 Wien, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstra\u00c3\u009fe 8-10, 1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstra\u00dfe 8-10, 1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6531,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.71859715,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"85","issue":"297","first_page":"119","last_page":"152"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9998000264167786,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9986000061035156,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9970999956130981,"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":0.8909403085708618},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6204228401184082},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5571178197860718},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.548740565776825},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5446583032608032},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5375238656997681},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5372241735458374},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.526646614074707},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4862317144870758},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4775015711784363},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4435514807701111},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.43302851915359497},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3799019455909729},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.25743842124938965},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10589820146560669},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10258352756500244},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08460360765457153},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07252192497253418}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8909403085708618},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6204228401184082},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5571178197860718},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.548740565776825},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5446583032608032},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5375238656997681},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5372241735458374},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.526646614074707},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4862317144870758},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4775015711784363},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4435514807701111},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.43302851915359497},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3799019455909729},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.25743842124938965},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10589820146560669},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10258352756500244},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08460360765457153},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07252192497253418},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/2990","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/2990","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1311.5028","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1311.5028","pdf_url":"https://arxiv.org/pdf/1311.5028","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1311.5028","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1311.5028","pdf_url":"https://arxiv.org/pdf/1311.5028","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":68,"referenced_works":["https://openalex.org/W8052360","https://openalex.org/W80638212","https://openalex.org/W145511199","https://openalex.org/W1425400007","https://openalex.org/W1501778161","https://openalex.org/W1513198935","https://openalex.org/W1569304948","https://openalex.org/W1584657480","https://openalex.org/W1602383637","https://openalex.org/W1602760118","https://openalex.org/W1604809219","https://openalex.org/W1940191795","https://openalex.org/W1965482218","https://openalex.org/W1968376936","https://openalex.org/W1969720662","https://openalex.org/W1971285640","https://openalex.org/W1973246593","https://openalex.org/W1977294297","https://openalex.org/W1980808567","https://openalex.org/W1982115588","https://openalex.org/W1989056711","https://openalex.org/W1989911287","https://openalex.org/W1990081118","https://openalex.org/W1991670087","https://openalex.org/W1991896659","https://openalex.org/W2009272201","https://openalex.org/W2009985306","https://openalex.org/W2013901196","https://openalex.org/W2016858086","https://openalex.org/W2018419001","https://openalex.org/W2024506048","https://openalex.org/W2026949835","https://openalex.org/W2036564429","https://openalex.org/W2037870010","https://openalex.org/W2040740620","https://openalex.org/W2053656257","https://openalex.org/W2059998776","https://openalex.org/W2060449697","https://openalex.org/W2062444320","https://openalex.org/W2062583795","https://openalex.org/W2073469129","https://openalex.org/W2075490698","https://openalex.org/W2078645506","https://openalex.org/W2079598795","https://openalex.org/W2086279700","https://openalex.org/W2088527939","https://openalex.org/W2106150226","https://openalex.org/W2122137889","https://openalex.org/W2125439985","https://openalex.org/W2132820941","https://openalex.org/W2136689980","https://openalex.org/W2141921161","https://openalex.org/W2144098834","https://openalex.org/W2156164638","https://openalex.org/W2491010324","https://openalex.org/W2496081756","https://openalex.org/W2610857016","https://openalex.org/W2748789952","https://openalex.org/W2950678188","https://openalex.org/W2951818655","https://openalex.org/W2963683362","https://openalex.org/W4245007249","https://openalex.org/W4285719527","https://openalex.org/W4292079583","https://openalex.org/W4293238311","https://openalex.org/W4294988936","https://openalex.org/W4306156108","https://openalex.org/W4309408314"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W2793786119","https://openalex.org/W1972759654"],"abstract_inverted_index":{"We":[0,169],"consider":[1],"the":[2,6,55,81,145,200,205,216],"question":[3],"of":[4,54,104,130,219],"approximating":[5],"inverse":[7],"<inline-formula":[8,59,84,105,149,172,220],"content-type=\"math/mathml\">":[9,60,85,106,150,173,221],"<mml:math":[10,61,86,107,151,174,222],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[11,62,87,108,152,175,223],"alttext=\"bold":[12,63,109,153,176,224],"upper":[13,17,64,110,154,177,225],"W":[14,47],"equals":[15],"bold":[16],"V":[18],"Superscript":[19],"negative":[20],"1\">":[21],"<mml:semantics>":[22,66,90,112,156,179,227],"<mml:mrow>":[23],"<mml:mrow":[24,31,36,67,113,157,180,228],"class=\"MJX-TeXAtom-ORD\">":[25,32,37,68,114,158,181,229],"<mml:mi":[26,33,69,115,159,182,230],"mathvariant=\"bold\">W</mml:mi>":[27,116,183],"</mml:mrow>":[28,35,42,44,71,117,161,184,232],"<mml:mo>=</mml:mo>":[29],"<mml:msup>":[30],"mathvariant=\"bold\">V</mml:mi>":[34,70,160,231],"<mml:mo>":[38],"\u2212":[39],"</mml:mo>":[40],"<mml:mn>1</mml:mn>":[41],"</mml:msup>":[43],"<mml:annotation":[45,72,92,118,162,185,233],"encoding=\"application/x-tex\">\\mathbf":[46,73,119,163,186,234],"=":[48],"\\mathbf":[49],"V^{-1}</mml:annotation>":[50],"</mml:semantics>":[51,75,94,121,165,188,236],"</mml:math>":[52,76,95,122,166,189,237],"</inline-formula>":[53,77,96,123,167,190,238],"Galerkin":[56],"stiffness":[57],"matrix":[58],"V\">":[65,89,155,226],"V</mml:annotation>":[74,164,235],"obtained":[78],"by":[79,194],"discretizing":[80],"simple-layer":[82],"operator":[83,148],"alttext=\"upper":[88],"<mml:mi>V</mml:mi>":[91],"encoding=\"application/x-tex\">V</mml:annotation>":[93],"with":[97,140],"piecewise":[98],"constant":[99],"functions.":[100],"The":[101],"block":[102,206],"partitioning":[103],"W\">":[111,178],"W</mml:annotation>":[120,187],"is":[124],"assumed":[125],"to":[126,143],"satisfy":[127],"any":[128],"one":[129],"several":[131],"standard":[132],"admissibility":[133],"criteria":[134],"that":[135,171,199],"are":[136,213],"employed":[137],"in":[138,204],"connection":[139],"clustering":[141],"algorithms":[142],"approximate":[144],"discrete":[146],"BEM":[147],".":[168,239],"show":[170],"can":[191],"be":[192],"approximated":[193],"blockwise":[195],"low-rank":[196],"matrices":[197],"such":[198],"error":[201],"decays":[202],"exponentially":[203],"rank":[207],"employed.":[208],"Similar":[209],"exponential":[210],"approximability":[211],"results":[212],"shown":[214],"for":[215],"Cholesky":[217],"factorization":[218]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}
