Advertisement

Matrix completion with e-algorithm

In memory of Peter Wynn (1931–2017)
  • Walter Gander
  • Qiquan Shi
Original Paper
  • 19 Downloads

Abstract

We show in this paper how the convergence of an algorithm for matrix completion can be significantly improved by applying Wynn’s e-algorithm. Straightforward generalization of the scalar e-algorithm to matrices fails. However, accelerating the convergence of only the missing matrix elements turns out to be very successful.

Keywords

Convergence acceleration Epsilon-algorithm Matrix completion 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Brezinski, C.: Accélération de la Convergence en Analyse Numérique. Lecture Notes in Mathematics, p 584. Springer, Berlin (1977)CrossRefGoogle Scholar
  2. 2.
    Brezinski, C.: Généralisations de la transformation de Shanks, de la table de Padé et de l’e-algorithme. Calcolo 12, 317–360 (1975)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Brezinski, C., Redivo-Zaglia, M.: The simplified topological epsilon-algorithms for accelerating sequences in a vector space. SIAM J. Sci. Comput. 36, A2227–A2247 (2014)CrossRefMATHGoogle Scholar
  4. 4.
    Brezinski, C., Redivo-Zaglia, M.: The simplified topological epsilon-algorithms: software and applications. Numer. Algorithms 74, 1237–1260 (2017)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Brezinski, C., Redivo-Zaglia, M.: The genesis and early developments of Aitken’s process, Shanks’ transformation, the e–algorithm, and related fixed point methods. Numer. Algorithms, this issueGoogle Scholar
  6. 6.
    Candès, E. J., Recht, B.: Exact matrix completion via convex optimization. Found. Comput. Math. 9(6), 717–772 (2009)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Gander, W, Gander, M.J., Kwok, F.: Scientific Computing, an Introduction Using Maple and Matlab. Springer, Berlin (2014)CrossRefMATHGoogle Scholar
  8. 8.
    McLeod, JB: A note on the e-algorithm. Computing 7(1–2), 17–24 (1971)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Sidi A: Vector extrapolation methods with applications. Number 17 in SIAM series on Computational Science and Engineering. SIAM (2017)Google Scholar
  10. 10.
    Shanks, D: Non-linear transformation of divergent and slowly convergent sequences. J. Math. Phys. 34, 1–42 (1955)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Shi Q, Lu, H, Cheung Y-M: Rank-one matrix completion with automatic rank estimation via L1-norm regularization. IEEE Trans. Neural Netw. Learn Syst. PP(99), 1–14 (2017).  https://doi.org/10.1109/TNNLS.2017.2766160. In pressGoogle Scholar
  12. 12.
    Wynn, P.: On a device for computing the e m(S n)-transformation. MTAC 10, 91–96 (1956)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceETH ZurichZurichSwitzerland
  2. 2.Department of Computer ScienceHKBUKowloon TongHong Kong

Personalised recommendations