{"id":"https://openalex.org/W1980528419","doi":"https://doi.org/10.1137/100812574","title":"Exponential Convergence of Gauss--Jacobi Quadratures for Singular Integrals over Simplices in Arbitrary Dimension","display_name":"Exponential Convergence of Gauss--Jacobi Quadratures for Singular Integrals over Simplices in Arbitrary Dimension","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1980528419","doi":"https://doi.org/10.1137/100812574","mag":"1980528419"},"language":"en","primary_location":{"id":"doi:10.1137/100812574","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100812574","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/A5062089780","display_name":"Alexey Chernov","orcid":"https://orcid.org/0000-0002-5527-803X"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Alexey Chernov","raw_affiliation_strings":["Hausdorff Center for Mathematics and Institute for Numerical Simulation, University of Bonn, 53115 Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Hausdorff Center for Mathematics and Institute for Numerical Simulation, University of Bonn, 53115 Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110448103","display_name":"Christoph Schwab","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Christoph Schwab","raw_affiliation_strings":["Seminar f\u00fcr Angewandte Mathematik, ETH Z\u00fcrich, 8092 Z\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Seminar f\u00fcr Angewandte Mathematik, ETH Z\u00fcrich, 8092 Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062089780"],"corresponding_institution_ids":["https://openalex.org/I135140700"],"apc_list":null,"apc_paid":null,"fwci":0.6363,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.67614929,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"50","issue":"3","first_page":"1433","last_page":"1455"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9987000226974487,"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":0.9987000226974487,"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/T10514","display_name":"Numerical methods in engineering","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8752954602241516},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.6878558993339539},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5776656866073608},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5775647163391113},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.5573976039886475},{"id":"https://openalex.org/keywords/singular-integral","display_name":"Singular integral","score":0.5238328576087952},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5137094259262085},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.47280803322792053},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.43445730209350586},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.41358840465545654},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32192718982696533},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.1960904598236084},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.11587032675743103}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8752954602241516},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.6878558993339539},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5776656866073608},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5775647163391113},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.5573976039886475},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.5238328576087952},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5137094259262085},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.47280803322792053},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.43445730209350586},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.41358840465545654},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32192718982696533},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.1960904598236084},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.11587032675743103},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100812574","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100812574","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"},{"id":"pmh:oai:centaur.reading.ac.uk:33216","is_oa":false,"landing_page_url":"https://centaur.reading.ac.uk/view/creators/90005505.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4306402273","display_name":"CentAUR (University of Reading)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71052956","host_organization_name":"University of Reading","host_organization_lineage":["https://openalex.org/I71052956"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1532154335","https://openalex.org/W1550884118","https://openalex.org/W1560939910","https://openalex.org/W1972342898","https://openalex.org/W2006808706","https://openalex.org/W2032532622","https://openalex.org/W2033022456","https://openalex.org/W2047292749","https://openalex.org/W2069877263","https://openalex.org/W2073601238","https://openalex.org/W2144098834"],"related_works":["https://openalex.org/W3168586318","https://openalex.org/W3128284001","https://openalex.org/W2030322846","https://openalex.org/W1987395535","https://openalex.org/W1973321202","https://openalex.org/W2021597182","https://openalex.org/W3159111101","https://openalex.org/W4210699452","https://openalex.org/W2087018406","https://openalex.org/W2929787118"],"abstract_inverted_index":{"Galerkin":[0],"discretizations":[1],"of":[2,10,47,58,92,171],"integral":[3],"operators":[4],"in":[5,126,150,163],"$\\mathbb{R}^{d}$":[6],"require":[7],"the":[8,100,106,151,164,169,172,184],"evaluation":[9],"integrals":[11],"$\\int_{S^{(1)}}\\!\\int_{S^{(2)}}\\!f(x,y)\\,dydx$,":[12],"where":[13],"$S^{(1)},S^{(2)}$":[14],"are":[15],"$d$-dimensional":[16],"simplices":[17],"and":[18,31,78,128,180,192],"$f$":[19,60],"has":[20],"a":[21,45,56,116,142],"singularity":[22,118],"at":[23,65],"$x=y$.":[24],"In":[25,111],"[A.":[26,187],"Chernov,":[27,188],"T.":[28,189],"von":[29,190],"Petersdorff,":[30,191],"C.":[32,193],"Schwab,":[33,194],"M$2$AN":[34,195],"Math.":[35,196],"Model.":[36,197],"Numer.":[37,198],"Anal.,":[38,199],"45":[39,200],"(2011),":[40,201],"pp.":[41,202],"387--422]":[42],"we":[43,114],"constructed":[44],"family":[46],"$hp$-quadrature":[48],"rules":[49,175],"${Q}_N$":[50],"with":[51,69,105,120,135],"$N$":[52],"function":[53],"evaluations":[54],"for":[55,62,81,87],"class":[57],"integrands":[59],"allowing":[61],"algebraic":[63],"singularities":[64],"$x=y$,":[66],"possibly":[67],"nonintegrable":[68],"respect":[70],"to":[71,183],"either":[72],"$dx$":[73],"or":[74],"$dy$":[75],"(hypersingular":[76],"kernels)":[77],"Gevrey-$\\delta$":[79],"smooth":[80],"$x\\ne":[82],"y$.":[83],"This":[84],"is":[85,139,148],"satisfied":[86],"kernels":[88],"from":[89,186],"broad":[90],"classes":[91],"pseudodifferential":[93],"operators.":[94],"We":[95,155,167],"proved":[96],"that":[97,130],"$Q_N$":[98],"achieves":[99],"exponential":[101],"convergence":[102,133],"rate":[103,134],"$\\mathcal{O}(\\exp(-rN^\\gamma))$":[104],"exponent":[107],"$\\gamma":[108,136],"=":[109,137],"1/(2d\\delta+1)$.":[110],"this":[112],"paper":[113],"consider":[115],"special":[117],"$\\|x-y\\|^\\alpha$":[119],"real":[121],"$\\alpha$":[122],"which":[123],"appears":[124],"frequently":[125],"appplication":[127],"prove":[129],"an":[131],"improved":[132],"1/(2d\\delta)$":[138],"achieved":[140],"if":[141],"certain":[143],"one-dimensional":[144],"Gauss--Jacobi":[145,161,174],"quadrature":[146],"rule":[147],"used":[149],"(univariate)":[152],"\u201esingular":[153],"coordinate.\u201d":[154],"also":[156],"analyze":[157],"approximation":[158],"by":[159],"tensor":[160],"quadratures":[162],"\u201eregular":[165],"coordinates.\u201d":[166],"illustrate":[168],"performance":[170],"new":[173],"on":[176],"several":[177],"numerical":[178],"examples":[179],"compare":[181],"it":[182],"$hp$-quadratures":[185],"387--422].":[203]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
