{"id":"https://openalex.org/W2963860305","doi":"https://doi.org/10.1007/s10915-018-0825-4","title":"Computing Integrals Involved the Gaussian Function with a Small Standard Deviation","display_name":"Computing Integrals Involved the Gaussian Function with a Small Standard Deviation","publication_year":2018,"publication_date":"2018-09-15","ids":{"openalex":"https://openalex.org/W2963860305","doi":"https://doi.org/10.1007/s10915-018-0825-4","mag":"2963860305"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-018-0825-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-018-0825-4","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of 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/A5100711444","display_name":"Yunyun Ma","orcid":"https://orcid.org/0000-0001-7435-2824"},"institutions":[{"id":"https://openalex.org/I2799850029","display_name":"Dongguan University of Technology","ror":"https://ror.org/01m8p7q42","country_code":"CN","type":"education","lineage":["https://openalex.org/I2799850029"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunyun Ma","raw_affiliation_strings":["School of Computer Science and Network Security, Dongguan University of Technology, Dongguan, 523808, People\u2019s Republic of China","School of Computer Science and Network Security, Dongguan University of Technology, Dongguan, 523808, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Network Security, Dongguan University of Technology, Dongguan, 523808, People\u2019s Republic of China","institution_ids":["https://openalex.org/I2799850029"]},{"raw_affiliation_string":"School of Computer Science and Network Security, Dongguan University of Technology, Dongguan, 523808, People's Republic of China","institution_ids":["https://openalex.org/I2799850029"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026572582","display_name":"Yuesheng Xu","orcid":"https://orcid.org/0000-0003-3965-3087"},"institutions":[{"id":"https://openalex.org/I81365321","display_name":"Old Dominion University","ror":"https://ror.org/04zjtrb98","country_code":"US","type":"education","lineage":["https://openalex.org/I81365321"]},{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN","US"],"is_corresponding":true,"raw_author_name":"Yuesheng Xu","raw_affiliation_strings":["Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, 23529, USA","School of Data and Computer Science, and Guangdong Province Key Lab of Computational Science, Sun Yat-sen University, Guangzhou, 510275, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, 23529, USA","institution_ids":["https://openalex.org/I81365321"]},{"raw_affiliation_string":"School of Data and Computer Science, and Guangdong Province Key Lab of Computational Science, Sun Yat-sen University, Guangzhou, 510275, People\u2019s Republic of China","institution_ids":["https://openalex.org/I157773358"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026572582"],"corresponding_institution_ids":["https://openalex.org/I157773358","https://openalex.org/I81365321"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.643,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71735376,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"78","issue":"3","first_page":"1744","last_page":"1767"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9976999759674072,"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":0.9976999759674072,"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/T11405","display_name":"Geophysics and Gravity Measurements","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9911999702453613,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.8653742074966431},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8382683992385864},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.7567996382713318},{"id":"https://openalex.org/keywords/gauss\u2013kronrod-quadrature-formula","display_name":"Gauss\u2013Kronrod quadrature formula","score":0.6439345479011536},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6041006445884705},{"id":"https://openalex.org/keywords/clenshaw\u2013curtis-quadrature","display_name":"Clenshaw\u2013Curtis quadrature","score":0.594612181186676},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5696015357971191},{"id":"https://openalex.org/keywords/adaptive-quadrature","display_name":"Adaptive quadrature","score":0.5601965188980103},{"id":"https://openalex.org/keywords/tanh-sinh-quadrature","display_name":"Tanh-sinh quadrature","score":0.5510761737823486},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5355494022369385},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5234726667404175},{"id":"https://openalex.org/keywords/gauss\u2013hermite-quadrature","display_name":"Gauss\u2013Hermite quadrature","score":0.5174620747566223},{"id":"https://openalex.org/keywords/gauss\u2013laguerre-quadrature","display_name":"Gauss\u2013Laguerre quadrature","score":0.4815428853034973},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.45211800932884216},{"id":"https://openalex.org/keywords/standard-deviation","display_name":"Standard deviation","score":0.4460490643978119},{"id":"https://openalex.org/keywords/weight-function","display_name":"Weight function","score":0.440665066242218},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4335160553455353},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.20055004954338074},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.14743846654891968},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.06738585233688354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06539455056190491},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06389966607093811}],"concepts":[{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.8653742074966431},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8382683992385864},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.7567996382713318},{"id":"https://openalex.org/C14103991","wikidata":"https://www.wikidata.org/wiki/Q5527852","display_name":"Gauss\u2013Kronrod quadrature formula","level":4,"score":0.6439345479011536},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6041006445884705},{"id":"https://openalex.org/C172657837","wikidata":"https://www.wikidata.org/wiki/Q5131618","display_name":"Clenshaw\u2013Curtis quadrature","level":5,"score":0.594612181186676},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5696015357971191},{"id":"https://openalex.org/C184599523","wikidata":"https://www.wikidata.org/wiki/Q4680758","display_name":"Adaptive quadrature","level":4,"score":0.5601965188980103},{"id":"https://openalex.org/C162046254","wikidata":"https://www.wikidata.org/wiki/Q7683194","display_name":"Tanh-sinh quadrature","level":5,"score":0.5510761737823486},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5355494022369385},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5234726667404175},{"id":"https://openalex.org/C167590341","wikidata":"https://www.wikidata.org/wiki/Q5527850","display_name":"Gauss\u2013Hermite quadrature","level":5,"score":0.5174620747566223},{"id":"https://openalex.org/C6866599","wikidata":"https://www.wikidata.org/wiki/Q4218412","display_name":"Gauss\u2013Laguerre quadrature","level":5,"score":0.4815428853034973},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.45211800932884216},{"id":"https://openalex.org/C22679943","wikidata":"https://www.wikidata.org/wiki/Q159375","display_name":"Standard deviation","level":2,"score":0.4460490643978119},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.440665066242218},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4335160553455353},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.20055004954338074},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.14743846654891968},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.06738585233688354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06539455056190491},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06389966607093811},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-018-0825-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-018-0825-4","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5600000023841858,"display_name":"No poverty","id":"https://metadata.un.org/sdg/1"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W640428934","https://openalex.org/W1152352997","https://openalex.org/W1230456367","https://openalex.org/W1496426756","https://openalex.org/W1496738390","https://openalex.org/W1529218607","https://openalex.org/W1550884118","https://openalex.org/W1592150738","https://openalex.org/W1969270341","https://openalex.org/W2028783611","https://openalex.org/W2053166411","https://openalex.org/W2061744138","https://openalex.org/W2064878889","https://openalex.org/W2072273591","https://openalex.org/W2073732659","https://openalex.org/W2076221890","https://openalex.org/W2081633643","https://openalex.org/W2099371695","https://openalex.org/W2144181355","https://openalex.org/W2152535248","https://openalex.org/W2157005274","https://openalex.org/W2238549287","https://openalex.org/W2313299119","https://openalex.org/W2314359380","https://openalex.org/W2393935934","https://openalex.org/W2417626906","https://openalex.org/W2568618671","https://openalex.org/W2751862591","https://openalex.org/W2801179766","https://openalex.org/W2963082050","https://openalex.org/W2995136929","https://openalex.org/W2998559157","https://openalex.org/W4229868531","https://openalex.org/W4230104858","https://openalex.org/W4230941884","https://openalex.org/W4252559437","https://openalex.org/W4253937035","https://openalex.org/W4254630587","https://openalex.org/W4299432846","https://openalex.org/W4300223101","https://openalex.org/W4301441647"],"related_works":["https://openalex.org/W4294281846","https://openalex.org/W4377005030","https://openalex.org/W2550867510","https://openalex.org/W2929787118","https://openalex.org/W2289189603","https://openalex.org/W4380609151","https://openalex.org/W4317584040","https://openalex.org/W4225983467","https://openalex.org/W4377968225","https://openalex.org/W2963494703"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}