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Newton-like Polynomial-Coded Distributed Computing for Numerical Stability.

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Název: Newton-like Polynomial-Coded Distributed Computing for Numerical Stability.
Autoři: Dai, Mingjun, Lai, Xiong, Tong, Yanli, Li, Bingchun
Zdroj: Symmetry (20738994); Jul2023, Vol. 15 Issue 7, p1372, 12p
Témata: VANDERMONDE matrices, DISTRIBUTED computing, POLYNOMIALS
Abstrakt: For coded distributed computing (CDC), polynomial code is one prevalent encoding method for CDC (called Poly-CDC). It suffers from poor numerical stability due to the Vandermonde matrix serving as the coefficient matrix which needs to be inverted, and whose condition number increases exponentially with the size of the matrix or equivalently with the number of parallel worker nodes. To improve the numerical stability, especially for large networks, we propose a Newton-like polynomial code (NLPC)-based CDC (NLPC-CDC), with a design dedicated for both matrix–vector and matrix–matrix multiplications. The associated proof of the constructed code possesses a (n , k) -symmetrical combination property (CP), where symmetrical means the worker nodes have identical computation volume, CP means the k-symmetrical original computing tasks are encoded into n (n ≥ k) -symmetrically coded computing tasks, and the arbitrary k resulting from the n-coded computing tasks can recover the intended computing results. Extensive numerical studies verify the significant numerical stability improvement of our proposed NLPC-CDC over Poly-CDC. [ABSTRACT FROM AUTHOR]
Copyright of Symmetry (20738994) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Newton-like Polynomial-Coded Distributed Computing for Numerical Stability.
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  Data: <searchLink fieldCode="AR" term="%22Dai%2C+Mingjun%22">Dai, Mingjun</searchLink><br /><searchLink fieldCode="AR" term="%22Lai%2C+Xiong%22">Lai, Xiong</searchLink><br /><searchLink fieldCode="AR" term="%22Tong%2C+Yanli%22">Tong, Yanli</searchLink><br /><searchLink fieldCode="AR" term="%22Li%2C+Bingchun%22">Li, Bingchun</searchLink>
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  Data: Symmetry (20738994); Jul2023, Vol. 15 Issue 7, p1372, 12p
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  Data: <searchLink fieldCode="DE" term="%22VANDERMONDE+matrices%22">VANDERMONDE matrices</searchLink><br /><searchLink fieldCode="DE" term="%22DISTRIBUTED+computing%22">DISTRIBUTED computing</searchLink><br /><searchLink fieldCode="DE" term="%22POLYNOMIALS%22">POLYNOMIALS</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: For coded distributed computing (CDC), polynomial code is one prevalent encoding method for CDC (called Poly-CDC). It suffers from poor numerical stability due to the Vandermonde matrix serving as the coefficient matrix which needs to be inverted, and whose condition number increases exponentially with the size of the matrix or equivalently with the number of parallel worker nodes. To improve the numerical stability, especially for large networks, we propose a Newton-like polynomial code (NLPC)-based CDC (NLPC-CDC), with a design dedicated for both matrix–vector and matrix–matrix multiplications. The associated proof of the constructed code possesses a (n , k) -symmetrical combination property (CP), where symmetrical means the worker nodes have identical computation volume, CP means the k-symmetrical original computing tasks are encoded into n (n ≥ k) -symmetrically coded computing tasks, and the arbitrary k resulting from the n-coded computing tasks can recover the intended computing results. Extensive numerical studies verify the significant numerical stability improvement of our proposed NLPC-CDC over Poly-CDC. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Symmetry (20738994) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.3390/sym15071372
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      – Code: eng
        Text: English
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        PageCount: 12
        StartPage: 1372
    Subjects:
      – SubjectFull: VANDERMONDE matrices
        Type: general
      – SubjectFull: DISTRIBUTED computing
        Type: general
      – SubjectFull: POLYNOMIALS
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      – TitleFull: Newton-like Polynomial-Coded Distributed Computing for Numerical Stability.
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              M: 07
              Text: Jul2023
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              Y: 2023
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