{"id":"https://openalex.org/W2924319069","doi":"https://doi.org/10.1109/isit.2019.8849468","title":"Numerically Stable Polynomially Coded Computing","display_name":"Numerically Stable Polynomially Coded Computing","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2924319069","doi":"https://doi.org/10.1109/isit.2019.8849468","mag":"2924319069"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2019.8849468","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849468","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1903.08326","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012930356","display_name":"Mohammad Fahim","orcid":"https://orcid.org/0000-0002-4266-7087"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mohammad Fahim","raw_affiliation_strings":["Department of Electrical Engineering, Pennsylvania State University","Department of Electrical Engineering , The Pennsylvania State University , University Park, PA , USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Pennsylvania State University","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Electrical Engineering , The Pennsylvania State University , University Park, PA , USA","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008627075","display_name":"Viveck R. Cadambe","orcid":"https://orcid.org/0000-0001-6786-8785"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Viveck R. Cadambe","raw_affiliation_strings":["Department of Electrical Engineering, Pennsylvania State University","Department of Electrical Engineering , The Pennsylvania State University , University Park, PA , USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Pennsylvania State University","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Electrical Engineering , The Pennsylvania State University , University Park, PA , USA","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012930356"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":null,"apc_paid":null,"fwci":0.3714,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.62877649,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"67","issue":"5","first_page":"2758","last_page":"2785"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10772","display_name":"Distributed systems and fault tolerance","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/vandermonde-matrix","display_name":"Vandermonde matrix","score":0.9675266742706299},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6992311477661133},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.5954592227935791},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.5081417560577393},{"id":"https://openalex.org/keywords/monomial-basis","display_name":"Monomial basis","score":0.5063940286636353},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48613497614860535},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44171345233917236},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.43775755167007446},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3899663984775543},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37838441133499146},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.177358478307724},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07627934217453003}],"concepts":[{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.9675266742706299},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6992311477661133},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.5954592227935791},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.5081417560577393},{"id":"https://openalex.org/C46132437","wikidata":"https://www.wikidata.org/wiki/Q6901742","display_name":"Monomial basis","level":3,"score":0.5063940286636353},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48613497614860535},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44171345233917236},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.43775755167007446},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3899663984775543},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37838441133499146},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.177358478307724},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07627934217453003},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/isit.2019.8849468","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849468","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"doi:10.1109/tit.2021.3050526","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3050526","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1903.08326","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.08326","pdf_url":"https://arxiv.org/pdf/1903.08326","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":"","raw_type":"text"},{"id":"mag:2924319069","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1903.08326","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},{"id":"doi:10.48550/arxiv.1903.08326","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1903.08326","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1903.08326","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.08326","pdf_url":"https://arxiv.org/pdf/1903.08326","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5044918678","display_name":null,"funder_award_id":"CCF 1763657","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2924319069.pdf","grobid_xml":"https://content.openalex.org/works/W2924319069.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W253307310","https://openalex.org/W1576347883","https://openalex.org/W1970821516","https://openalex.org/W1988043369","https://openalex.org/W1989782579","https://openalex.org/W2021311647","https://openalex.org/W2078114900","https://openalex.org/W2083613288","https://openalex.org/W2089238086","https://openalex.org/W2108789132","https://openalex.org/W2268702383","https://openalex.org/W2745045892","https://openalex.org/W2784935051","https://openalex.org/W2886967976","https://openalex.org/W2902687529","https://openalex.org/W2911546317","https://openalex.org/W2962208489","https://openalex.org/W2962813697","https://openalex.org/W2962957061","https://openalex.org/W2963117124","https://openalex.org/W2963138848","https://openalex.org/W2963597099","https://openalex.org/W2964160151","https://openalex.org/W2975971390","https://openalex.org/W2976462019","https://openalex.org/W2976645076","https://openalex.org/W3103649678","https://openalex.org/W3111688502","https://openalex.org/W4244681853","https://openalex.org/W4320800818","https://openalex.org/W6730190955","https://openalex.org/W6738835244","https://openalex.org/W6742061381","https://openalex.org/W6748342376","https://openalex.org/W6751815326","https://openalex.org/W6752191310","https://openalex.org/W6752557422","https://openalex.org/W6758630230","https://openalex.org/W6787029084"],"related_works":["https://openalex.org/W113406481","https://openalex.org/W2963687969","https://openalex.org/W3118694039","https://openalex.org/W2033961328","https://openalex.org/W2108888104","https://openalex.org/W3126626028","https://openalex.org/W2200283591","https://openalex.org/W200948783","https://openalex.org/W2074967544","https://openalex.org/W2503997773","https://openalex.org/W1254304998","https://openalex.org/W90191732","https://openalex.org/W1965952671","https://openalex.org/W2950389159","https://openalex.org/W2953020094","https://openalex.org/W2061547567","https://openalex.org/W2273701522","https://openalex.org/W2952159834","https://openalex.org/W2353687675","https://openalex.org/W3101523321"],"abstract_inverted_index":{"We":[0,123,144],"study":[1],"the":[2,27,46,51,61,80,150,168],"numerical":[3,132,186],"stability":[4],"of":[5,18,29,64,69,141,161,170],"polynomial":[6,98],"based":[7,99],"encoding":[8],"methods,":[9],"which":[10,138],"has":[11],"emerged":[12],"to":[13,101,135,148,183,190],"be":[14],"a":[15,157,174],"powerful":[16],"class":[17],"techniques":[19,118],"for":[20,41,91,110,119],"providing":[21],"straggler":[22],"and":[23,56,104,154,173],"fault":[24],"tolerance":[25,49],"in":[26],"area":[28],"coded":[30,120,163],"computing.":[31,164],"Our":[32,165,178],"contributions":[33],"are":[34],"as":[35,50,85,188],"follows:":[36],"1)We":[37],"construct":[38,114],"new":[39,115],"codes":[40],"matrix":[42,121],"multiplication":[43],"that":[44,60,126],"achieve":[45],"same":[47],"fault/straggler":[48],"previously":[52],"constructed":[53],"MatDot":[54],"Codes":[55],"Polynomial":[57],"Codes.2)We":[58],"show":[59],"condition":[62,107],"number":[63,108],"every":[65],"m":[66,71,75],"\u00d7m":[67],"sub-matrix":[68],"an":[70],"\u00d7n,":[72],"n":[73,92],"\u2265":[74],"Chebyshev-Vandermonde":[76,111],"matrix,":[77],"evaluated":[78],"on":[79],"n-point":[81],"Chebyshev":[82,102],"grid,":[83],"grows":[84],"O(n":[86],"<sup":[87],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[88],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2(n-m)</sup>":[89],")":[90],">":[93],"m.3)By":[94],"specializing":[95],"our":[96,106,127,146],"orthogonal":[97],"constructions":[100,128,147],"polynomials,":[103],"using":[105],"bound":[109],"matrices,":[112],"we":[113],"numerically":[116,158],"stable":[117,159],"multiplication.":[122],"empirically":[124,182],"demonstrate":[125],"have":[129,184],"significantly":[130],"lower":[131,185],"errors":[133,187],"compared":[134,189],"previous":[136],"approaches":[137],"involve":[139],"inversion":[140],"Vandermonde":[142],"matrices.":[143],"generalize":[145],"explore":[149],"trade-off":[151],"between":[152],"computation/communication":[153],"fault-tolerance.4)We":[155],"propose":[156],"specialization":[160],"Lagrange":[162],"approach":[166,179],"involves":[167],"choice":[169],"evaluation":[171],"points":[172],"suitable":[175],"decoding":[176],"procedure.":[177],"is":[180],"demonstrated":[181],"standard":[191],"methods.":[192]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}