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Algorithms for polynomial division

  • Dario Bini
  • Victor Pan
Algebraic Algorithms I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 204)

Keywords

Algebraic Extension Arbitrary Field Depth Circuit Fast Matrix Polynomial Division 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [B]
    D. Bini, Parallel Solution of Certain Toeplitz Linear Systems, SIAM J. Comp. 13, 2, 268–276 (1984), also T.R.B82-04 I.E.I. of C.N.R., Pisa, Italy (April 1982).Google Scholar
  2. [BPa]
    D. Bini, V. Pan, Fast Parallel Polynomial Division via Reduction to Triangular Toeplitz Matrix Inversion and to Polynomial Inversion Modulo a Power Tech. Rep. 84-11, Computer Sci. Dept., SUNY, Albany, NY (1984).Google Scholar
  3. [BPb]
    D. Bini, V. Pan, Fast Parallel Algorithms for Polynomial Division over Arbitrary Fields of Constants, Nota Interna, Dept. of Informatica, University of Pisa, Pisa, Italy (August 1984).Google Scholar
  4. [E]
    W. Eberly, Very Fast Parallel Matrix and Polynomial Arithmetic, Proc. 25-th Ann. IEEE Symp. FOCS, 21–30 (1984).Google Scholar
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    C.M. Fiduccia, Fast Matrix Multiplication, Proc. 3-rd Ann. Symp. Theory of Computing, 45–49 (1971).Google Scholar
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    D.E. Knuth, The Art of Computer Programming, v. 2, Addison-Wesley (1981).Google Scholar
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    J.C. Lafon Base Tensorielle des matrices de Hankel (ou de Toeplitz), Applications. Numer. Math. 23, 249–361 (1975).Google Scholar
  8. [P80]
    V. Pan, The Bit-Operation Complexity of the Convolution of Vectors and of the DFT, Tech. Rep. 80-6, Computer Sci. Dept., SUNY, Albany, NY (1980).Google Scholar
  9. [P84]
    V. Pan, How to Multiply Matrices Faster, Lecture Notes in Computer Science, v. 179, Springer-Verlag (1984).Google Scholar
  10. [R]
    J. Reif, Logarithmic Depth Circuits for Algebraic Functions, Proc. 23-rd Ann. IEEE Symp. FOCS, 138–145 (1983).Google Scholar
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    A. Schönhage, Asymptotically Fast Algorithms for the Numerical Multiplication and Division of Polynomials with Complex Coefficients, Proc. EUROCAM, Marseille (1982).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Dario Bini
    • 1
  • Victor Pan
    • 2
  1. 1.University of PisaPisaItaly
  2. 2.SUNY AlbanyAlbanyUSA

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