{"id":"https://openalex.org/W2010625137","doi":"https://doi.org/10.1137/s0097539798337613","title":"Checking Approximate Computations of Polynomials and Functional Equations","display_name":"Checking Approximate Computations of Polynomials and Functional Equations","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2010625137","doi":"https://doi.org/10.1137/s0097539798337613","mag":"2010625137"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539798337613","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539798337613","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 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/A5033348209","display_name":"Funda Erg\u00fcn","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Funda Erg\u00fcn","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100903522","display_name":"S. Ravi Kumar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Ravi Kumar","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041567023","display_name":"Ronitt Rubinfeld","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ronitt Rubinfeld","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5033348209"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.13997358,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"31","issue":"2","first_page":"550","last_page":"576"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9944000244140625,"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/multilinear-map","display_name":"Multilinear map","score":0.7855663299560547},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.6310122609138489},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5613115429878235},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5399639010429382},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.44277510046958923},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.425035297870636},{"id":"https://openalex.org/keywords/functional-equation","display_name":"Functional equation","score":0.42227545380592346},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3765532672405243},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3721664547920227},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.367147296667099},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2871716618537903},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22876015305519104},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.16921758651733398},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09418925642967224}],"concepts":[{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.7855663299560547},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.6310122609138489},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5613115429878235},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5399639010429382},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.44277510046958923},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.425035297870636},{"id":"https://openalex.org/C153576954","wikidata":"https://www.wikidata.org/wiki/Q594452","display_name":"Functional equation","level":3,"score":0.42227545380592346},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3765532672405243},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3721664547920227},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.367147296667099},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2871716618537903},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22876015305519104},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.16921758651733398},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09418925642967224},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0097539798337613","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539798337613","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.25.7389","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.7389","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://external.nj.nec.com/homepages/ronitt/papers/approx.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W125170976","https://openalex.org/W1236790333","https://openalex.org/W1482096325","https://openalex.org/W1484889287","https://openalex.org/W1487800348","https://openalex.org/W1498798784","https://openalex.org/W1501278571","https://openalex.org/W1512638263","https://openalex.org/W1518938643","https://openalex.org/W1596412683","https://openalex.org/W1965720095","https://openalex.org/W1965921504","https://openalex.org/W1980280740","https://openalex.org/W1989959848","https://openalex.org/W1993677455","https://openalex.org/W1996839061","https://openalex.org/W2003874621","https://openalex.org/W2005722951","https://openalex.org/W2007225893","https://openalex.org/W2018925011","https://openalex.org/W2019578639","https://openalex.org/W2049069037","https://openalex.org/W2064489546","https://openalex.org/W2064968474","https://openalex.org/W2080793339","https://openalex.org/W2097206148","https://openalex.org/W2129638800","https://openalex.org/W2146584722","https://openalex.org/W2148352980","https://openalex.org/W2151603610","https://openalex.org/W2808650095","https://openalex.org/W3004537778","https://openalex.org/W4229601877","https://openalex.org/W4256317935"],"related_works":["https://openalex.org/W1999178348","https://openalex.org/W4296311369","https://openalex.org/W4318719034","https://openalex.org/W37958683","https://openalex.org/W2396820687","https://openalex.org/W3035010459","https://openalex.org/W3151212431","https://openalex.org/W2011892585","https://openalex.org/W1524101012","https://openalex.org/W4251748586"],"abstract_inverted_index":{"A":[0],"majority":[1],"of":[2,24,44,60,75,90,97,108,208,216,227],"the":[3,16,39,79,91,109,185,198,206,214,224],"results":[4,18,65,220],"on":[5,95,114],"self-testing":[6],"and":[7,26,54,73,104,124,144,156,201],"correcting":[8],"deal":[9,48],"with":[10,49],"programs":[11,31,45,190],"which":[12],"purport":[13],"to":[14,29,38,68,151,188],"compute":[15,33],"correct":[17,40],"precisely.":[19],"We":[20,63,134,147],"relax":[21],"this":[22,136],"notion":[23],"correctness":[25],"show":[27,149,183],"how":[28,67,150],"check":[30],"that":[32,46,161,184],"only":[34],"a":[35,81,166],"numerical":[36],"approximation":[37],"answer.":[41],"The":[42],"types":[43,59],"we":[47,182,204],"are":[50,194],"those":[51,159],"computing":[52],"polynomials":[53],"functions":[55,160,193],"defined":[56],"by":[57,84,137,169],"certain":[58],"functional":[61,211,228],"equations.":[62,229],"present":[64],"showing":[66],"perform":[69,152],"approximate":[70,140,153,199,217],"checking,":[71,154],"self-testing,":[72,155],"self-correcting":[74,157],"polynomials,":[76],"settling":[77,165],"in":[78,213],"affirmative":[80],"question":[82,167],"raised":[83,168],"[P.":[85],"Gemmell":[86],"et":[87],"al.,":[88],"Proceedings":[89,107],"23rd":[92],"ACM":[93],"Symposium":[94,113],"Theory":[96],"Computing,":[98],"1991,":[99],"pp.":[100,120,132,177],"32--42;":[101],"R.":[102,122],"Rubinfeld":[103,123],"M.":[105,125],"Sudan,":[106,126],"Third":[110],"Annual":[111],"ACM-SIAM":[112],"Discrete":[115],"Algorithms,":[116],"Orlando,":[117],"FL,":[118],"1992,":[119],"23--43;":[121],"SIAM":[127,172],"J.":[128,173],"Comput.,":[129,174],"25":[130],"(1996),":[131],"252--271].":[133],"obtain":[135],"first":[138],"building":[139],"self-testers":[141],"for":[142,158,191,223],"linear":[143],"multilinear":[145],"functions.":[146],"then":[148],"satisfy":[162],"addition":[163],"theorems,":[164],"[R.":[170],"Rubinfeld,":[171],"28":[175],"(1999),":[176],"1972--1997].":[178],"In":[179],"both":[180,195],"cases,":[181],"properties":[186],"used":[187],"test":[189],"these":[192],"robust":[196],"(in":[197],"sense)":[200],"stable.":[202],"Finally,":[203],"explore":[205],"use":[207],"reductions":[209],"between":[210],"equations":[212],"context":[215],"self-testing.":[218],"Our":[219],"have":[221],"implications":[222],"stability":[225],"theory":[226]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
