{"id":"https://openalex.org/W2073469129","doi":"https://doi.org/10.1137/090775932","title":"On the Numerical Rank of the Off-Diagonal Blocks of Schur Complements of Discretized Elliptic PDEs","display_name":"On the Numerical Rank of the Off-Diagonal Blocks of Schur Complements of Discretized Elliptic PDEs","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2073469129","doi":"https://doi.org/10.1137/090775932","mag":"2073469129"},"language":"en","primary_location":{"id":"doi:10.1137/090775932","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090775932","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/A5009022144","display_name":"Shivkumar Chandrasekaran","orcid":"https://orcid.org/0000-0003-2508-5605"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Chandrasekaran","raw_affiliation_strings":["shiv@ece.ucsb.edu and naveen@umail.ucsb.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"shiv@ece.ucsb.edu and naveen@umail.ucsb.edu#TAB#","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035921496","display_name":"P. Dewilde","orcid":"https://orcid.org/0000-0002-9553-1845"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"P. Dewilde","raw_affiliation_strings":["p.dewilde@ewi.tudelft.nl#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"p.dewilde@ewi.tudelft.nl#TAB#","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103226688","display_name":"Ming Gu","orcid":"https://orcid.org/0009-0005-2951-5256"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Gu","raw_affiliation_strings":["mgu@math.berkeley.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"mgu@math.berkeley.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067488925","display_name":"Naveen Somasunderam","orcid":"https://orcid.org/0000-0003-0592-0896"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"N. Somasunderam","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.466,"has_fulltext":false,"cited_by_count":78,"citation_normalized_percentile":{"value":0.9460159,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"31","issue":"5","first_page":"2261","last_page":"2290"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9983999729156494,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9839000105857849,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9022977352142334},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7384648323059082},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.6571287512779236},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.6449558734893799},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5935970544815063},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5399060845375061},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5027480125427246},{"id":"https://openalex.org/keywords/schurs-theorem","display_name":"Schur's theorem","score":0.49590763449668884},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4627971649169922},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3309438228607178},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.28932952880859375},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18635594844818115},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.06704902648925781}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9022977352142334},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7384648323059082},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.6571287512779236},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6449558734893799},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5935970544815063},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5399060845375061},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5027480125427246},{"id":"https://openalex.org/C29701004","wikidata":"https://www.wikidata.org/wiki/Q1786292","display_name":"Schur's theorem","level":5,"score":0.49590763449668884},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4627971649169922},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3309438228607178},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28932952880859375},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18635594844818115},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.06704902648925781},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.0},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/090775932","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090775932","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.418.2962","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.418.2962","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ens.ewi.tudelft.nl/pubs/dewilde10siam.pdf","raw_type":"text"},{"id":"pmh:oai:tudelft.nl:uuid:2a0a5c4e-300a-45ca-8536-806f8b2109cb","is_oa":false,"landing_page_url":"http://resolver.tudelft.nl/uuid:2a0a5c4e-300a-45ca-8536-806f8b2109cb","pdf_url":null,"source":{"id":"https://openalex.org/S4306400906","display_name":"Research Repository (Delft University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98358874","host_organization_name":"Delft University of Technology","host_organization_lineage":["https://openalex.org/I98358874"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","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":16,"referenced_works":["https://openalex.org/W1482537073","https://openalex.org/W1487444668","https://openalex.org/W1973786815","https://openalex.org/W2009849678","https://openalex.org/W2018419001","https://openalex.org/W2025076058","https://openalex.org/W2035476608","https://openalex.org/W2060449697","https://openalex.org/W2062028527","https://openalex.org/W2075085615","https://openalex.org/W2083206954","https://openalex.org/W2113679823","https://openalex.org/W2156164638","https://openalex.org/W2610857016","https://openalex.org/W3039626672","https://openalex.org/W4253945327"],"related_works":["https://openalex.org/W2146459776","https://openalex.org/W1975201729","https://openalex.org/W2055747065","https://openalex.org/W2083715084","https://openalex.org/W1549544714","https://openalex.org/W1972018154","https://openalex.org/W2522358176","https://openalex.org/W2085886596","https://openalex.org/W105891345","https://openalex.org/W2394451470"],"abstract_inverted_index":{"It":[0],"is":[1,32,58],"shown":[2,50],"that":[3,17],"the":[4,8,20,39,46],"numerical":[5,56],"rank":[6,57],"of":[7,11,15,23,38],"off-diagonal":[9,53],"blocks":[10,54],"certain":[12],"Schur":[13,47],"complements":[14,48],"matrices":[16],"arise":[18],"from":[19],"finite-difference":[21],"discretization":[22],"constant":[24,36],"coefficient,":[25],"elliptic":[26],"PDEs":[27],"in":[28,43],"two":[29],"spatial":[30],"dimensions":[31],"bounded":[33],"by":[34],"a":[35,59],"independent":[37],"grid":[40],"size.":[41],"Moreover,":[42],"three-dimensional":[44],"problems":[45],"are":[49],"to":[51],"have":[52],"whose":[55],"slowly":[60],"growing":[61],"function.":[62]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
