{"id":"https://openalex.org/W3092040120","doi":"https://doi.org/10.1137/20m1373037","title":"Computation of the Complex Error Function Using Modified Trapezoidal Rules","display_name":"Computation of the Complex Error Function Using Modified Trapezoidal Rules","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3092040120","doi":"https://doi.org/10.1137/20m1373037","mag":"3092040120"},"language":"en","primary_location":{"id":"doi:10.1137/20m1373037","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1373037","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":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2010.05659.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061999498","display_name":"Mohammad Al Azah","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mohammad Al Azah","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5037304012","display_name":"Simon N. Chandler\u2010Wilde","orcid":"https://orcid.org/0000-0003-0578-1283"},"institutions":[{"id":"https://openalex.org/I71052956","display_name":"University of Reading","ror":"https://ror.org/05v62cm79","country_code":"GB","type":"education","lineage":["https://openalex.org/I71052956"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Simon N. Chandler-Wilde","raw_affiliation_strings":["#N#University of Reading#N#"],"affiliations":[{"raw_affiliation_string":"#N#University of Reading#N#","institution_ids":["https://openalex.org/I71052956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061999498"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02827661,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"5","first_page":"2346","last_page":"2367"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9944999814033508,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.7923024892807007},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.7747381925582886},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6298288702964783},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5731105804443359},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5175849199295044},{"id":"https://openalex.org/keywords/error-function","display_name":"Error function","score":0.49316853284835815},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46867403388023376},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.44866642355918884},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.42503973841667175},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.4212053716182709},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41198480129241943},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3210653066635132},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3209133744239807},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28284454345703125},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.14440834522247314},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1287722885608673},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11733201146125793},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.09319519996643066}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7923024892807007},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.7747381925582886},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6298288702964783},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5731105804443359},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5175849199295044},{"id":"https://openalex.org/C202286095","wikidata":"https://www.wikidata.org/wiki/Q579262","display_name":"Error function","level":2,"score":0.49316853284835815},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46867403388023376},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.44866642355918884},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.42503973841667175},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.4212053716182709},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41198480129241943},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3210653066635132},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3209133744239807},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28284454345703125},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.14440834522247314},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1287722885608673},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11733201146125793},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.09319519996643066},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/20m1373037","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1373037","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:98904","is_oa":false,"landing_page_url":"https://centaur.reading.ac.uk/view/creators/90000890.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"},{"id":"mag:3092040120","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2010.05659.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:3092040120","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2010.05659.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":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/W1505276458","https://openalex.org/W1541633373","https://openalex.org/W1552202016","https://openalex.org/W1971922216","https://openalex.org/W1972597916","https://openalex.org/W1988533746","https://openalex.org/W1997924127","https://openalex.org/W1998527589","https://openalex.org/W2019266959","https://openalex.org/W2040841120","https://openalex.org/W2042312320","https://openalex.org/W2045566155","https://openalex.org/W2046802345","https://openalex.org/W2048373032","https://openalex.org/W2066650934","https://openalex.org/W2067931600","https://openalex.org/W2072707186","https://openalex.org/W2077527931","https://openalex.org/W2086092605","https://openalex.org/W2086350070","https://openalex.org/W2120062331","https://openalex.org/W2164933087","https://openalex.org/W2785266995","https://openalex.org/W2789098417","https://openalex.org/W4238052875"],"related_works":["https://openalex.org/W2073443629","https://openalex.org/W2049100078","https://openalex.org/W2028212620","https://openalex.org/W2945951333","https://openalex.org/W2766250208","https://openalex.org/W3212754271","https://openalex.org/W153451723","https://openalex.org/W3125331871","https://openalex.org/W2952271648","https://openalex.org/W2021186990","https://openalex.org/W2060773871","https://openalex.org/W2162590460","https://openalex.org/W3098640252","https://openalex.org/W1969795824","https://openalex.org/W2153288151","https://openalex.org/W2124822546","https://openalex.org/W2020928358","https://openalex.org/W818909869","https://openalex.org/W2319072435","https://openalex.org/W3015023967"],"abstract_inverted_index":{"In":[0],"this":[1,115,140],"paper":[2],"we":[3,71,75],"propose":[4],"a":[5,81],"method":[6,32,142],"for":[7,153,156],"computing":[8,154],"the":[9,24,31,85,101,106,128],"Faddeeva":[10],"function":[11,82],"$w(z)":[12],":=":[13],"\\re^{-z^2}\\erfc(-\\ri\\,z)$":[14],"via":[15],"truncated":[16],"modified":[17],"trapezoidal":[18],"rule":[19],"approximations":[20,73],"to":[21,34],"integrals":[22],"on":[23],"real":[25],"line.":[26],"Our":[27],"starting":[28],"point":[29],"is":[30,134,143],"due":[33],"Matta":[35],"and":[36,45,47,147],"Reichel":[37],"({\\em":[38,49,61],"Math.\\":[39,50],"Comp.}":[40,51],"{\\bf":[41,52,67],"25}":[42],"(1971),":[43],"pp.~339--344)":[44],"Hunter":[46],"Regan":[48],"26}":[53],"(1972),":[54],"pp.~339--541).":[55],"Addressing":[56],"shortcomings":[57],"flagged":[58],"by":[59,117],"Weideman":[60],"SIAM.\\":[62],"J.\\":[63],"Numer.\\":[64],"Anal.":[65],"}":[66],"31}":[68],"(1994),":[69],"pp.~1497--1518),":[70],"construct":[72],"which":[74,93],"prove":[76],"are":[77,109],"exponentially":[78],"convergent":[79],"as":[80],"of":[83,87,97,103],"$N+1$,":[84],"number":[86],"quadrature":[88],"points,":[89],"obtaining":[90],"error":[91],"bounds":[92],"show":[94],"that":[95,139],"accuracies":[96],"$2\\times":[98],"10^{-15}$":[99],"in":[100,145],"computation":[102,148],"$w(z)$":[104,133,155],"throughout":[105,127],"complex":[107,130,157],"plane":[108],"achieved":[110],"with":[111,150],"$N":[112],"=":[113],"11$,":[114],"confirmed":[116],"computations.":[118],"These":[119],"approximations,":[120],"moreover,":[121],"provably":[122],"achieve":[123],"small":[124],"relative":[125],"errors":[126],"upper":[129],"half-plane":[131],"where":[132],"non-zero.":[135],"Numerical":[136],"tests":[137],"suggest":[138],"new":[141],"competitive,":[144],"accuracy":[146],"times,":[149],"existing":[151],"methods":[152],"$z$.":[158]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}