Faster Algorithms for Multivariate Interpolation With Multiplicities and Simultaneous Polynomial Approximations
The interpolation step in the Guruswami-Sudan algorithm is a bivariate interpolation problem with multiplicities commonly solved in the literature using either structured linear algebra or basis reduction of polynomial lattices. This problem has been extended to three or more variables; for this gen...
Saved in:
| Published in | IEEE transactions on information theory Vol. 61; no. 5; pp. 2370 - 2387 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.05.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9448 1557-9654 1557-9654 |
| DOI | 10.1109/TIT.2015.2416068 |
Cover
| Abstract | The interpolation step in the Guruswami-Sudan algorithm is a bivariate interpolation problem with multiplicities commonly solved in the literature using either structured linear algebra or basis reduction of polynomial lattices. This problem has been extended to three or more variables; for this generalization, all fast algorithms proposed so far rely on the lattice approach. In this paper, we reduce this multivariate interpolation problem to a problem of simultaneous polynomial approximations, which we solve using fast structured linear algebra. This improves the best known complexity bounds for the interpolation step of the list-decoding of Reed-Solomon codes, Parvaresh-Vardy codes, and folded Reed-Solomon codes. In particular, for Reed-Solomon list-decoding with re-encoding, our approach has complexity O ~ (ℓ ω-1 m 2 (n - k)), where ℓ, m, n, and k are the list size, the multiplicity, the number of sample points, and the dimension of the code, and ω is the exponent of linear algebra; this accelerates the previously fastest known algorithm by a factor of ℓ/m. |
|---|---|
| AbstractList | The interpolation step in the Guruswami-Sudan algorithm is a bivariate interpolation problem with multiplicities commonly solved in the literature using either structured linear algebra or basis reduction of polynomial lattices. This problem has been extended to three or more variables; for this generalization, all fast algorithms proposed so far rely on the lattice approach. In this paper, we reduce this multivariate interpolation problem to a problem of simultaneous polynomial approximations, which we solve using fast structured linear algebra. This improves the best known complexity bounds for the interpolation step of the list-decoding of Reed-Solomon codes, Parvaresh-Vardy codes, and folded Reed-Solomon codes. In particular, for Reed-Solomon list-decoding with re-encoding, our approach has complexity O ~ (ℓ ω-1 m 2 (n - k)), where ℓ, m, n, and k are the list size, the multiplicity, the number of sample points, and the dimension of the code, and ω is the exponent of linear algebra; this accelerates the previously fastest known algorithm by a factor of ℓ/m. The interpolation step in the Guruswami-Sudan algorithm is a bivariate interpolation problem with multiplicities commonly solved in the literature using either structured linear algebra or basis reduction of polynomial lattices. This problem has been extended to three or more variables; for this generalization, all fast algorithms proposed so far rely on the lattice approach. In this paper, we reduce this multivariate interpolation problem to a problem of simultaneous polynomial approximations, which we solve using fast structured linear algebra. This improves the best known complexity bounds for the interpolation step of the list-decoding of Reed-Solomon codes, Parvaresh-Vardy codes, and folded Reed-Solomon codes. In particular, for Reed-Solomon list-decoding with re-encoding, our approach has complexity ..., where ..., and k are the list size, the multiplicity, the number of sample points, and the dimension of the code, and \omega is the exponent of linear algebra; this accelerates the previously fastest known algorithm by a factor of ... (ProQuest: ... denotes formulae/symbols omitted.) The interpolation step in the Guruswami-Sudan algorithm is a bivariateinterpolation problem with multiplicities commonly solved in the literatureusing either structured linear algebra or basis reduction of polynomiallattices. This problem has been extended to three or more variables; for thisgeneralization, all fast algorithms proposed so far rely on the latticeapproach. In this paper, we reduce this multivariate interpolation problem to aproblem of simultaneous polynomial approximations, which we solve using faststructured linear algebra. This improves the best known complexity bounds forthe interpolation step of the list-decoding of Reed-Solomon codes,Parvaresh-Vardy codes, and folded Reed-Solomon codes. In particular, forReed-Solomon list-decoding with re-encoding, our approach has complexity$\mathcal{O}\tilde{~}(\ell^{\omega-1}m^2(n-k))$, where $\ell,m,n,k$ are thelist size, the multiplicity, the number of sample points and the dimension ofthe code, and $\omega$ is the exponent of linear algebra; this accelerates thepreviously fastest known algorithm by a factor of $\ell / m$. |
| Author | Jeannerod, Claude-Pierre Schost, Eric Neiger, Vincent Chowdhury, Muhammad F. I. Villard, Gilles |
| Author_xml | – sequence: 1 givenname: Muhammad F. I. surname: Chowdhury fullname: Chowdhury, Muhammad F. I. email: mchowdh3@csd.uwo.ca organization: Department of Computer Science, University of Western Ontario, London, ON, Canada – sequence: 2 givenname: Claude-Pierre surname: Jeannerod fullname: Jeannerod, Claude-Pierre email: claude-pierre.jeannerod@inria.fr organization: Laboratoire de l’Informatique du Parallélisme, (CNRS, ENS de Lyon, Inria, UCBL), Université de Lyon, Lyon, France – sequence: 3 givenname: Vincent surname: Neiger fullname: Neiger, Vincent email: vincent.neiger@ens-lyon.fr organization: Department of Computer Science, University of Western Ontario, London, ON, Canada – sequence: 4 givenname: Eric surname: Schost fullname: Schost, Eric email: eschost@uwo.ca organization: Department of Computer Science, University of Western Ontario, London, ON, Canada – sequence: 5 givenname: Gilles surname: Villard fullname: Villard, Gilles email: gilles.villard@ens-lyon.fr organization: Laboratoire de l’Informatique du Parallélisme, (CNRS, ENS de Lyon, Inria, UCBL), Université de Lyon, Lyon, France |
| BackLink | https://inria.hal.science/hal-00941435$$DView record in HAL |
| BookMark | eNptkc9rHCEYhqWkkE3ae6AXoaceZqvjj9HjEppmYUsL2dCjOBNtDK5O1Um6_33dTEhh6UnU55H3ez0DJyEGA8AFRkuMkfy8XW-XLcJs2VLMERdvwAIz1jWSM3oCFghh0UhKxSk4y_mhbinD7QLEK52LSXDlf8Xkyv0uQxsT_Db54h51croYuA6VGKPXxcUAf1Zqvh-9G1xxJkMd7uCN29VDHUycMvwR_T7EndMersYxxT9u92znd-Ct1T6b9y_rObi9-rK9vG4237-uL1ebZiC8K41lVAspNLG8FVYiTlBv7TBQ2lNhqewN6ztuSG_EHTGYWyYlbqmlHGNhMCPnAM_vTmHU-yftvRpTDZH2CiN1aEwVV9ShMfXSWHU-zc69_kdH7dT1aqMOZwhJiilhj21lP85sHe73ZHJRD3FKoY6kMO845R1pSaX4TA0p5pyMVbWw5yJK0s6_RqmfdxwFHYnH6f-jfJgVZ4x5xTvEWdtx8hdxWKbO |
| CODEN | IETTAW |
| CitedBy_id | crossref_primary_10_1109_TIT_2022_3140678 crossref_primary_10_3390_wevj14090245 crossref_primary_10_1016_j_jsc_2016_11_015 crossref_primary_10_1016_j_jco_2021_101574 crossref_primary_10_1109_TCOMM_2019_2927207 crossref_primary_10_1109_TCOMM_2022_3215998 crossref_primary_10_2197_ipsjjip_27_245 crossref_primary_10_1109_TCOMM_2020_3011991 crossref_primary_10_1137_16M1062855 crossref_primary_10_1109_TIT_2022_3188843 crossref_primary_10_3934_amc_2015_9_311 |
| Cites_doi | 10.1109/TIT.2007.911222 10.1007/3-540-11607-9_3 10.1145/1993886.1993931 10.1016/0020-0190(78)90067-4 10.1007/978-3-642-25405-5_13 10.1016/j.jsc.2008.01.002 10.1007/BF01178683 10.1109/TIT.2003.819332 10.1016/0377-0427(92)90039-Z 10.1515/crll.1936.175.50 10.1145/190347.190431 10.1016/j.tcs.2008.05.014 10.1109/18.490540 10.1016/j.jsc.2011.09.006 10.1109/TIT.2010.2096034 10.1145/322217.322225 10.1109/18.133246 10.1145/120694.120697 10.1145/860854.860889 10.1109/TIT.2011.2162160 10.1109/ITW.2003.1216682 10.1109/TIT.2005.850097 10.1017/CBO9781139856065 10.1007/978-1-4612-0129-8 10.1145/2608628.2608664 10.1109/ISIT.2006.261691 10.1145/2213977.2214056 10.1109/TIT.2008.926355 10.1109/18.817522 10.1109/SFCS.2005.29 10.1145/301250.301311 10.1007/978-3-642-57189-3_20 10.2140/obs.2013.1.271 10.1109/TIT.2010.2053901 10.1109/ICASSP.1980.1171074 10.1016/0024-3795(80)90161-5 10.1007/3-540-54522-0_93 10.1109/18.782097 10.1109/TIT.2013.2243800 10.1006/jcom.1997.0439 10.1016/j.jsc.2010.03.010 10.1007/3-540-09519-5_73 10.1016/S0747-7171(08)80013-2 10.1137/S0895479892230031 |
| ContentType | Journal Article |
| Copyright | Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) May 2015 Distributed under a Creative Commons Attribution 4.0 International License |
| Copyright_xml | – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) May 2015 – notice: Distributed under a Creative Commons Attribution 4.0 International License |
| DBID | 97E RIA RIE AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D 1XC VOOES ADTOC UNPAY |
| DOI | 10.1109/TIT.2015.2416068 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Hyper Article en Ligne (HAL) Hyper Article en Ligne (HAL) (Open Access) Unpaywall for CDI: Periodical Content Unpaywall |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Technology Research Database |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/ sourceTypes: Publisher – sequence: 2 dbid: UNPAY name: Unpaywall url: https://proxy.k.utb.cz/login?url=https://unpaywall.org/ sourceTypes: Open Access Repository |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science Mathematics |
| EISSN | 1557-9654 |
| EndPage | 2387 |
| ExternalDocumentID | oai:HAL:hal-00941435v2 3669037341 10_1109_TIT_2015_2416068 7065276 |
| Genre | orig-research Feature |
| GrantInformation_xml | – fundername: International Mobility Grant Explo’ra Doc through the Région Rhône-Alpes – fundername: Canada Research Chairs; Canada Research Chairs Program funderid: 10.13039/501100001804 – fundername: ANR through the HPAC project grantid: ANR 11 BS02 013 – fundername: Natural Sciences and Engineering Research Council of Canada; NSERC funderid: 10.13039/501100000038 |
| GroupedDBID | -~X .DC 0R~ 29I 3EH 4.4 5GY 5VS 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABFSI ABQJQ ABVLG ACGFO ACGFS ACGOD ACIWK AENEX AETEA AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 E.L EBS EJD F5P HZ~ H~9 IAAWW IBMZZ ICLAB IDIHD IFIPE IFJZH IPLJI JAVBF LAI M43 MS~ O9- OCL P2P PQQKQ RIA RIE RNS RXW TAE TN5 VH1 VJK AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D 1XC VOOES ADTOC UNPAY |
| ID | FETCH-LOGICAL-c367t-f54a898a3f628f90630bffcc44b48f49be5b76e3be8d3e16f599124f46118e153 |
| IEDL.DBID | UNPAY |
| ISSN | 0018-9448 1557-9654 |
| IngestDate | Wed Aug 20 00:21:13 EDT 2025 Sat Oct 25 11:16:31 EDT 2025 Sun Oct 05 00:24:30 EDT 2025 Wed Oct 01 02:55:10 EDT 2025 Thu Apr 24 23:00:06 EDT 2025 Wed Aug 27 08:31:32 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Keywords | Reed-Solomon codes structured matrix Multivariate polynomial interpolation polynomial approximation list decoding Multivariate interpolation List-decoding Structured matrices Fast algorithms |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0 other-oa |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c367t-f54a898a3f628f90630bffcc44b48f49be5b76e3be8d3e16f599124f46118e153 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 |
| ORCID | 0000-0003-1936-7155 0000-0002-8311-9490 |
| OpenAccessLink | https://proxy.k.utb.cz/login?url=https://inria.hal.science/hal-00941435v2/file/MultivariateInterpolation-PolyApprox_v2.pdf |
| PQID | 1676467323 |
| PQPubID | 36024 |
| PageCount | 18 |
| ParticipantIDs | unpaywall_primary_10_1109_tit_2015_2416068 proquest_journals_1676467323 hal_primary_oai_HAL_hal_00941435v2 crossref_citationtrail_10_1109_TIT_2015_2416068 crossref_primary_10_1109_TIT_2015_2416068 ieee_primary_7065276 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2015-05-01 |
| PublicationDateYYYYMMDD | 2015-05-01 |
| PublicationDate_xml | – month: 05 year: 2015 text: 2015-05-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | IEEE transactions on information theory |
| PublicationTitleAbbrev | TIT |
| PublicationYear | 2015 |
| Publisher | IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers |
| Publisher_xml | – name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) – name: Institute of Electrical and Electronics Engineers |
| References | ref15 reinhard (ref41) 2003 ref14 ref52 ref11 ref54 ref17 chowdhury (ref12) 0 ref16 storjohann (ref47) 2006 ref19 ref18 zeh (ref53) 2013 cohn (ref13) 2011 nielsen (ref36) 2013 ref51 ref50 bernstein (ref6) 2011; 7071 ref46 ref45 ref44 ref43 ref49 ref8 ref7 ref4 ref3 ref5 mceliece (ref33) 2003 ref40 roth (ref42) 2007 ref35 ref37 ref31 ref30 ref32 zippel (ref55) 1979; 72 ref2 ref1 ref39 brander (ref9) 2010 ref38 busse (ref10) 2008 ref23 ref26 ref25 ref20 ref22 ref21 ref28 ref27 hasse (ref24) 1936; 1936 ref29 stothers (ref48) 2010 möller (ref34) 1982; 144 |
| References_xml | – ident: ref22 doi: 10.1109/TIT.2007.911222 – volume: 144 start-page: 24 year: 1982 ident: ref34 article-title: The construction of multivariate polynomials with preassigned zeros publication-title: Computer Algebra doi: 10.1007/3-540-11607-9_3 – ident: ref44 doi: 10.1145/1993886.1993931 – ident: ref16 doi: 10.1016/0020-0190(78)90067-4 – volume: 7071 start-page: 200 year: 2011 ident: ref6 article-title: Simplified high-speed high-distance list decoding for alternant codes publication-title: Post-Quantum Cryptography doi: 10.1007/978-3-642-25405-5_13 – ident: ref32 doi: 10.1016/j.jsc.2008.01.002 – ident: ref11 doi: 10.1007/BF01178683 – ident: ref28 doi: 10.1109/TIT.2003.819332 – ident: ref2 doi: 10.1016/0377-0427(92)90039-Z – year: 2003 ident: ref41 article-title: Algorithme LLL polynomial et applications – year: 2007 ident: ref42 publication-title: Introduction to Coding Theory – volume: 1936 start-page: 50 year: 1936 ident: ref24 article-title: Theorie der höheren Differentiale in einem algebraischen Funktionenkörper mit vollkommenem Konstantenkörper bei beliebiger Charakteristik publication-title: J reine angew Math doi: 10.1515/crll.1936.175.50 – ident: ref25 doi: 10.1145/190347.190431 – ident: ref8 doi: 10.1016/j.tcs.2008.05.014 – ident: ref30 doi: 10.1109/18.490540 – start-page: 6271 year: 2006 ident: ref47 article-title: Notes on computing minimal approximant bases publication-title: Proc Challenges Symbolic Comput Softw – ident: ref21 doi: 10.1016/j.jsc.2011.09.006 – year: 2010 ident: ref9 article-title: Interpolation and list decoding of algebraic codes – ident: ref27 doi: 10.1109/TIT.2010.2096034 – ident: ref45 doi: 10.1145/322217.322225 – ident: ref17 doi: 10.1109/18.133246 – ident: ref46 doi: 10.1145/120694.120697 – ident: ref20 doi: 10.1145/860854.860889 – ident: ref54 doi: 10.1109/TIT.2011.2162160 – ident: ref29 doi: 10.1109/ITW.2003.1216682 – year: 2010 ident: ref48 article-title: On the complexity of matrix multiplication – ident: ref1 doi: 10.1109/TIT.2005.850097 – ident: ref19 doi: 10.1017/CBO9781139856065 – ident: ref39 doi: 10.1007/978-1-4612-0129-8 – ident: ref31 doi: 10.1145/2608628.2608664 – year: 2013 ident: ref36 article-title: List decoding of algebraic codes – ident: ref18 doi: 10.1109/ISIT.2006.261691 – year: 2008 ident: ref10 article-title: Multivariate list decoding of evaluation codes with a Gröbner basis perspective – ident: ref51 doi: 10.1145/2213977.2214056 – ident: ref52 doi: 10.1109/TIT.2008.926355 – ident: ref43 doi: 10.1109/18.817522 – ident: ref40 doi: 10.1109/SFCS.2005.29 – year: 2003 ident: ref33 article-title: The Guruswami-Sudan decoding algorithm for Reed-Solomon codes – ident: ref38 doi: 10.1145/301250.301311 – ident: ref37 doi: 10.1007/978-3-642-57189-3_20 – ident: ref14 doi: 10.2140/obs.2013.1.271 – ident: ref50 doi: 10.1109/TIT.2010.2053901 – ident: ref35 doi: 10.1109/ICASSP.1980.1171074 – ident: ref7 doi: 10.1016/0024-3795(80)90161-5 – year: 0 ident: ref12 article-title: On the complexity of multivariate interpolation with multiplicities and of simultaneous polynomial approximations – ident: ref26 doi: 10.1007/3-540-54522-0_93 – year: 2013 ident: ref53 article-title: Algebraic soft- and hard-decision decoding of generalized Reed-Solomon and cyclic codes – ident: ref23 doi: 10.1109/18.782097 – ident: ref5 doi: 10.1109/TIT.2013.2243800 – ident: ref49 doi: 10.1006/jcom.1997.0439 – start-page: 298 year: 2011 ident: ref13 article-title: Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding publication-title: Proc of Innovations in Computer Science – ident: ref4 doi: 10.1016/j.jsc.2010.03.010 – volume: 72 start-page: 216 year: 1979 ident: ref55 article-title: Probabilistic algorithms for sparse polynomials publication-title: Symbolic and Algebraic Computation doi: 10.1007/3-540-09519-5_73 – ident: ref15 doi: 10.1016/S0747-7171(08)80013-2 – ident: ref3 doi: 10.1137/S0895479892230031 |
| SSID | ssj0014512 |
| Score | 2.3498924 |
| Snippet | The interpolation step in the Guruswami-Sudan algorithm is a bivariate interpolation problem with multiplicities commonly solved in the literature using either... The interpolation step in the Guruswami-Sudan algorithm is a bivariateinterpolation problem with multiplicities commonly solved in the literatureusing either... |
| SourceID | unpaywall hal proquest crossref ieee |
| SourceType | Open Access Repository Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 2370 |
| SubjectTerms | Algorithms Computer Science Context Information Theory Interpolation Lattice theory Linear algebra Linear systems list decoding Mathematical problems Mathematics multivariate polynomial interpolation Polynomials Reed-Solomon codes structured matrix Symbolic Computation |
| SummonAdditionalLinks | – databaseName: IEEE Electronic Library (IEL) dbid: RIE link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1Rb9MwED6tewEeGGygZWzIQryASNskjpM8VhNVQQwh0Ym9RXZib9VCMq3Jxvj13MVJtAJCvFXtVXV19t13ue8-A7zWJvM01smujmTucmOkqyJuXBki1sBqTElBA84nn8XilH88C8-24N0wC6O1bslnekwv215-XmUNPSqbUEvOj8QIRlEs7KzW0DHgoWeVwT08wFhz9C3JaTJZflgShyscY7ZCvB5vpKDRBREg25tVNkDmg6a8kne3siju5Zv5Dpz0K7U0k8txU6tx9vM3Ecf__StP4HEHPNnM7pSnsKXLXdjpL3Vg3RnfhUf3FAr3oJpLUlJgs-K8ul7VF9_XDFEua8d2b7DMRqTKLG-xsqQ69g2t7OfUGW_1Wpksc_Z1RdxFWeqqWbMvVXFH89C0IBI1_7GyE5TrZ3A6f788XrjdHQ1uFoiodk3IZZzEMjDCj01CCl7KmCzjXPHY8ETpUEVCB0rHeaA9YUIEpD43XGBlozHcPoftsir1PrBE57nB5JiEJuEY9mKMJXnuR1M1VbnWkQOT3m1p1gmY0z0aRdoWMtMkRUen5Oi0c7QDb4ZvXFnxjn_YvsKdMJiR6vZi9iml94h9SbDyxndgj1w5WHVedOCw3zhpFwLWqScigVko8AMH3g6b6Y91YEzYWMfB33_iBTwkK0u1PITt-rrRRwiHavWyPQe_ACM1B4c priority: 102 providerName: IEEE |
| Title | Faster Algorithms for Multivariate Interpolation With Multiplicities and Simultaneous Polynomial Approximations |
| URI | https://ieeexplore.ieee.org/document/7065276 https://www.proquest.com/docview/1676467323 https://inria.hal.science/hal-00941435 https://inria.hal.science/hal-00941435v2/file/MultivariateInterpolation-PolyApprox_v2.pdf |
| UnpaywallVersion | submittedVersion |
| Volume | 61 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 1557-9654 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0014512 issn: 1557-9654 databaseCode: RIE dateStart: 19630101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9NAEB616QF6oNCCcCnVCnEBafOw12v7aCGigKCqRCLak7Vr7zYRxq6apKj99cz4RQISEgducTyWx97xzDfamW8AXhubjgzmydwEKuPCWsV1ICxXPmINzMa0ktTg_PlMTmbi44V_sQOXXS9Mge-9P0fc2USAAf7mVP9Ggf3WHRBd0aBqTr3FZBLxWF2cV9aVY_y8zO9iYuNGU8CUMbO7sCd9hOk92JudnceXtWfGj1xUk7UwnAY8kr5otzCHEc0dopovv4_RDfF9uBWydudUMFlNYtkCpQ_WxbW6-6HyfCM-jQ_gvn2yuizlW3-90v30_jfSx__y6I_hUYNqWVyb4RPYMcUhHLQTI1jjQA5hf4P-8AjKsSKaBhbnV-XNYjX_vmQIodnmvdnWzdlXlKrP07Z7RQbLVJGxLwsqjFSFKddLRhpSszUpVCm6qNszl09hNn4_fTfhzQAInnoyWHHrCxVGofKsdEMbET2YtjZNhdAitCLSxteBNJ42YeaZkbQ-ol1XWCExbTLoy59BrygL8xxYZLLMYuSNfBsJ9KkhOqosc4OhHurMmMCBQbvGSdqwo9OQjjypsqRhlEw_TBOyiqSxCgfedFdc18wgf5F9hWvZiRGl9yT-lNB_v9bXgSOyqk6KNqDdQDpw0lpZ0viXZTKSgcQQ57meA287y_tDD7TkLT2O_0X4BTykw7q68wR6q5u1eYkIbKVPqzbJ0-aL-gklhDLf |
| linkProvider | Unpaywall |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3fb9MwED5t42HsgcEGIjDAQryASNsktpM8Voiqg3ZCohN7i-zEZhVZMq3pYPz13OWXVkCIt6ixVVdn333X--4zwCtjU89gnuyaUGUut1a5OuTWVQKxBmZjWklqcJ6fyOkp_3Amzrbgbd8LY4ypyWdmQI91LT8r0zX9VTakkpwfym24IzjnounW6msGXHiNNriHRxizjq4oOYqHi-MFsbjEAOMVIvZoIwhtnxMFsr5bZQNm7q6LS3XzXeX5rYgz2Yd5t9aGaPJtsK70IP35m4zj__6Y-3CvhZ5s3OyVB7BligPY7651YO0pP4C9WxqFh1BOFGkpsHH-tbxaVucXK4Y4l9WNu9eYaCNWZQ1zsWxodewLjmreU228VmxlqsjY5yWxF1VhyvWKfSrzG-qIpgWRrPmPZdNDuXoIp5P3i3dTt72lwU0DGVauFVxFcaQCK_3IxqThpa1NU841jyyPtRE6lCbQJsoC40krEJL63HKJuY1Bh_sIdoqyMI-BxSbLLIbHWNiYo-OL0JtkmR-O9EhnxoQODDuzJWkrYU43aeRJncqM4gQNnZChk9bQDrzuZ1w28h3_GPsSd0I_jHS3p-NZQp8R_5KA5bXvwCGZsh_VWtGBo27jJK0TWCWeDCXGocAPHHjTb6Y_1oFeYWMdT_7-FS9gd7qYz5LZ8cnHp3CXZjTEyyPYqa7W5hmCo0o_r8_ELwzsCtQ |
| linkToUnpaywall | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9NAEB616QE4UGhBGApaIS4gbR72em0fLUQUEFSVSER7snbtXRJh7Kpxitpfz4xfJCAhceAWx2N57B3PfKOd-QbglbHpxGCezE2gMi6sVVwHwnLlI9bAbEwrSQ3On07lbCE-nPvne3DR98IU-N6HS8SdbQQY4W9O9W8U2K_dEdEVjerm1GtMJhGPNcV5ZVM5xs_K_CYmNm40BUwZM7sPB9JHmD6Ag8XpWXzReGb8yEU9WQvDacAj6YtuC3Mc0dwhqvnyhxjdEN-HOyFrf0kFk_Uklh1QemdTXKqbHyrPt-LT9BBuuydrylK-DTeVHqa3v5E-_pdHfwD3W1TL4sYMH8KeKY7gsJsYwVoHcgT3tugPj6GcKqJpYHH-tbxaVcvva4YQmm3fm-3cnH1BqeY8bbvXZLBMFRn7vKLCSFWYcrNmpCE1W5NCtaKrpj1z_QgW03fztzPeDoDgqSeDiltfqDAKlWelG9qI6MG0tWkqhBahFZE2vg6k8bQJM89MpPUR7brCColpk0Ff_hgGRVmYJ8Aik2UWI2_k20igTw3RUWWZG4z1WGfGBA6MujVO0pYdnYZ05EmdJY2jZP5-npBVJK1VOPC6v-KyYQb5i-xLXMtejCi9Z_HHhP77tb4OHJNV9VK0Ae0G0oGTzsqS1r-sk4kMJIY4z_UceNNb3h96oCXv6PH0X4SfwV06bKo7T2BQXW3Mc0RglX7Rfks_Afm9Md4 |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Faster+Algorithms+for+Multivariate+Interpolation+with+Multiplicities+and+Simultaneous+Polynomial+Approximations&rft.jtitle=IEEE+transactions+on+information+theory&rft.au=Chowdhury%2C+Muhammad+Foizul+Islam&rft.au=Jeannerod%2C+Claude-Pierre&rft.au=Neiger%2C+Vincent&rft.au=Schost%2C+Eric&rft.date=2015-05-01&rft.pub=Institute+of+Electrical+and+Electronics+Engineers&rft.issn=0018-9448&rft.spage=2370&rft.epage=2387&rft_id=info:doi/10.1109%2FTIT.2015.2416068&rft.externalDBID=HAS_PDF_LINK&rft.externalDocID=oai%3AHAL%3Ahal-00941435v2 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9448&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9448&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9448&client=summon |