{"id":"https://openalex.org/W1965827371","doi":"https://doi.org/10.1137/060659119","title":"Convergence of a Variant of the Zipper Algorithm for Conformal Mapping","display_name":"Convergence of a Variant of the Zipper Algorithm for Conformal Mapping","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1965827371","doi":"https://doi.org/10.1137/060659119","mag":"1965827371"},"language":"en","primary_location":{"id":"doi:10.1137/060659119","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060659119","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/A5022813432","display_name":"Donald E. Marshall","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Donald E. Marshall","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5006765366","display_name":"Steffen Rohde","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steffen Rohde","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022813432"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.2042,"has_fulltext":false,"cited_by_count":81,"citation_normalized_percentile":{"value":0.96822679,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"45","issue":"6","first_page":"2577","last_page":"2609"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11822","display_name":"Analytic and geometric function theory","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9697999954223633,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9650999903678894,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/conformal-map","display_name":"Conformal map","score":0.8062112331390381},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7909169793128967},{"id":"https://openalex.org/keywords/unit-disk","display_name":"Unit disk","score":0.6974267959594727},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6330593824386597},{"id":"https://openalex.org/keywords/jordan-curve-theorem","display_name":"Jordan curve theorem","score":0.544326901435852},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5398179292678833},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5330319404602051},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4599769115447998},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3939971625804901}],"concepts":[{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.8062112331390381},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7909169793128967},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.6974267959594727},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6330593824386597},{"id":"https://openalex.org/C70251129","wikidata":"https://www.wikidata.org/wiki/Q260928","display_name":"Jordan curve theorem","level":2,"score":0.544326901435852},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5398179292678833},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5330319404602051},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4599769115447998},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3939971625804901},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/060659119","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060659119","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:CiteSeerX.psu:10.1.1.100.2423","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.100.2423","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.washington.edu/~marshall/preprints/zipper.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1509839166","https://openalex.org/W1514537983","https://openalex.org/W1561974326","https://openalex.org/W1972525206","https://openalex.org/W1981344803","https://openalex.org/W1996288813","https://openalex.org/W2023413246","https://openalex.org/W2040827466","https://openalex.org/W2052645364","https://openalex.org/W2064685239","https://openalex.org/W2080402965","https://openalex.org/W2329563144","https://openalex.org/W2396879930","https://openalex.org/W2598582653"],"related_works":["https://openalex.org/W2083061485","https://openalex.org/W2997842411","https://openalex.org/W2015716952","https://openalex.org/W2392707140","https://openalex.org/W2519255911","https://openalex.org/W2028320454","https://openalex.org/W2016617075","https://openalex.org/W2953139458","https://openalex.org/W2138492073","https://openalex.org/W2038269350"],"abstract_inverted_index":{"In":[0],"the":[1,17,35,37,45,68,80,84,88,99,131],"early":[2],"1980s":[3],"an":[4,40,115],"elementary":[5],"algorithm":[6,21,38,111],"for":[7,64,87,118],"computing":[8],"conformal":[9,42,119],"maps":[10],"was":[11,28,112],"discovered":[12,113],"by":[13,52],"R.":[14],"K\u00fchnau":[15],"and":[16,24,74,83,91],"first":[18],"author.":[19],"The":[20,110],"is":[22],"fast":[23],"accurate,":[25],"but":[26],"convergence":[27,63],"not":[29],"known.":[30],"Given":[31],"points":[32,101],"$z_0,\\dots,z_n$":[33],"in":[34,67],"plane,":[36],"computes":[39],"explicit":[41],"map":[43],"of":[44,70,130],"unit":[46],"disk":[47],"onto":[48],"a":[49,53,104,108,128],"region":[50,82],"bounded":[51],"Jordan":[54,65],"curve":[55,106],"$\\gamma$":[56],"with":[57],"$z_0,\\dots,z_n":[58],"\\in":[59],"\\gamma$.":[60],"We":[61],"prove":[62],"regions":[66],"sense":[69],"uniformly":[71],"close":[72],"boundaries":[73],"give":[75],"corresponding":[76],"uniform":[77],"estimates":[78,95],"on":[79,103],"closed":[81,85],"disc":[86],"mapping":[89],"functions":[90],"their":[92],"inverses.":[93],"Improved":[94],"are":[96],"obtained":[97],"if":[98],"data":[100],"lie":[102],"$C^1$":[105],"or":[107],"K-quasicircle.":[109],"as":[114,127],"approximate":[116],"method":[117],"welding;":[120],"however,":[121],"it":[122],"can":[123],"also":[124],"be":[125],"viewed":[126],"discretization":[129],"Loewner":[132],"differential":[133],"equation.":[134]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}