{"id":"https://openalex.org/W2086325670","doi":"https://doi.org/10.1137/s1064827597328315","title":"A Stable Numerical Method for Inverting Shape from Moments","display_name":"A Stable Numerical Method for Inverting Shape from Moments","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2086325670","doi":"https://doi.org/10.1137/s1064827597328315","mag":"2086325670"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827597328315","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827597328315","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 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/A5110003399","display_name":"Gene H. Golub","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gene H. Golub","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002085979","display_name":"Peyman Milanfar","orcid":"https://orcid.org/0000-0003-1455-7662"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peyman Milanfar","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5001136231","display_name":"J. M. Varah","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"James Varah","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110003399"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.696,"has_fulltext":false,"cited_by_count":147,"citation_normalized_percentile":{"value":0.68070029,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"21","issue":"4","first_page":"1222","last_page":"1243"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11405","display_name":"Geophysics and Gravity Measurements","score":0.9979000091552734,"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"}},"topics":[{"id":"https://openalex.org/T11405","display_name":"Geophysics and Gravity Measurements","score":0.9979000091552734,"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/T12450","display_name":"Radio Astronomy Observations and Technology","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T13126","display_name":"Scientific Research and Discoveries","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7430015802383423},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6411073207855225},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5576844215393066},{"id":"https://openalex.org/keywords/gravimetry","display_name":"Gravimetry","score":0.5303709506988525},{"id":"https://openalex.org/keywords/gravitational-field","display_name":"Gravitational field","score":0.4829656183719635},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4720029830932617},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42335861921310425},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37305355072021484},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.35149258375167847},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.12669143080711365},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09492048621177673}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7430015802383423},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6411073207855225},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5576844215393066},{"id":"https://openalex.org/C202453963","wikidata":"https://www.wikidata.org/wiki/Q499964","display_name":"Gravimetry","level":3,"score":0.5303709506988525},{"id":"https://openalex.org/C14257148","wikidata":"https://www.wikidata.org/wiki/Q558066","display_name":"Gravitational field","level":2,"score":0.4829656183719635},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4720029830932617},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42335861921310425},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37305355072021484},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.35149258375167847},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.12669143080711365},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09492048621177673},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C166689943","wikidata":"https://www.wikidata.org/wiki/Q850283","display_name":"Interferometry","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s1064827597328315","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827597328315","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.160.5983","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.160.5983","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.let.uu.nl/~Hugo.Quene/personal/onderwijs/statistiek/stat0203.tentamen.antwoorden.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.30.9782","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.9782","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cse.ucsc.edu/~milanfar/SISC99.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.46.7116","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.7116","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cse.ucsc.edu/~milanfar/GMV_SIAM.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.49.7751","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.7751","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-sccm.stanford.edu/pub/sccm/sccm97-10.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W277879060","https://openalex.org/W1964061814","https://openalex.org/W1965328008","https://openalex.org/W1967486001","https://openalex.org/W1974818065","https://openalex.org/W1976248588","https://openalex.org/W1980177911","https://openalex.org/W1985263879","https://openalex.org/W2004917780","https://openalex.org/W2005229894","https://openalex.org/W2017889632","https://openalex.org/W2020804487","https://openalex.org/W2021311647","https://openalex.org/W2033332370","https://openalex.org/W2035990937","https://openalex.org/W2041091843","https://openalex.org/W2042255949","https://openalex.org/W2044008067","https://openalex.org/W2045126705","https://openalex.org/W2053039356","https://openalex.org/W2054658115","https://openalex.org/W2055673437","https://openalex.org/W2065656021","https://openalex.org/W2079239454","https://openalex.org/W2082987063","https://openalex.org/W2096710051","https://openalex.org/W2097883065","https://openalex.org/W2101276724","https://openalex.org/W2134192668","https://openalex.org/W2147522142","https://openalex.org/W2149523072","https://openalex.org/W2162654459","https://openalex.org/W2171369888","https://openalex.org/W2316418224","https://openalex.org/W2588992765","https://openalex.org/W2796908055","https://openalex.org/W2798909945","https://openalex.org/W3022909171","https://openalex.org/W3177790481","https://openalex.org/W4254559353"],"related_works":["https://openalex.org/W2101796708","https://openalex.org/W2079788077","https://openalex.org/W1637540481","https://openalex.org/W3013217431","https://openalex.org/W3089072748","https://openalex.org/W3087979403","https://openalex.org/W2182434736","https://openalex.org/W3207167641","https://openalex.org/W2181264966","https://openalex.org/W2551816988"],"abstract_inverted_index":{"We":[0,20],"derive":[1],"a":[2,71],"stable":[3],"technique,":[4],"based":[5],"upon":[6],"matrix":[7],"pencils,":[8],"for":[9],"the":[10,29,41,44,54,61,68],"reconstruction":[11],"of":[12,31,40,43,63,70,81],"(or":[13],"approximation":[14],"by)":[15],"polygonal":[16,36],"shapes":[17],"from":[18,79],"moments.":[19],"point":[21],"out":[22],"that":[23],"this":[24],"problem":[25,45,62],"can":[26],"be":[27,77],"considered":[28],"dual":[30],"2-D":[32],"numerical":[33,51],"quadrature":[34],"over":[35],"domains.":[37],"An":[38],"analysis":[39],"sensitivity":[42],"is":[46,65,75],"presented":[47],"along":[48],"with":[49],"some":[50],"examples":[52],"illustrating":[53],"relevant":[55],"points.":[56],"Finally,":[57],"an":[58],"application":[59],"to":[60,76],"gravimetry":[64],"explored":[66],"where":[67],"shape":[69],"gravitationally":[72],"anomalous":[73],"region":[74],"recovered":[78],"measurements":[80],"its":[82],"exterior":[83],"gravitational":[84],"field.":[85]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}