Improved parallel polynomial division and its extensions

@article{Bini1992ImprovedPP,
  title={Improved parallel polynomial division and its extensions},
  author={Dario Bini and Victor Y. Pan},
  journal={Proceedings., 33rd Annual Symposium on Foundations of Computer Science},
  year={1992},
  pages={131-136}
}
  • Dario Bini, V. Pan
  • Published 24 October 1992
  • Computer Science
  • Proceedings., 33rd Annual Symposium on Foundations of Computer Science
The authors compute the first N coefficients of the reciprocal r(x) of a given polynomial p(x), (r(x)p(x)=1 mod x/sup N/, p(0) not=0), by using, under the PRAM arithmetic models, O(h log N) time-steps and O((N/h)(1+2/sup -h/log/sup (h)/ N)) processors, for any h, h=1,2, . . .,log/sup */ N, provided that O(logm) steps and m processors suffice to perform DFT on m points and that log/sup (0)/ N=N, log/sup (h)/ N=log/sub 2/log/sup (h-1)/N, h=1, . . .,log/sup */N, log/sup */N=max(h:log/sup (h)/N>0… 
2 Citations

References

SHOWING 1-10 OF 15 REFERENCES
Polynomial division and its computational complexity
Parallel Solution of Certain Toeplitz Linear Systems
  • Dario Bini
  • Computer Science, Mathematics
    SIAM J. Comput.
  • 1984
TLDR
It is proved that if B is any matrix belonging to the algebra generated over the complex field by a given $n \times n$ matrix, then the system Bx = b can be solved with no more than $9\log n + 4$ steps with $O(n^2 )$ processors.
Supereffective slow-down of parallel computations
TLDR
A new technique is discussed, called supereffective slow-down, that yields quite fast an algorithm with work significantly smaller than that of the fastest algorithm for the same problem, and substantially improves the performance of the known parallel algorithms for triangular linear systems of equations.
Optimal size integer division circuits
Division is a fundamental problem for arithmetic and algebraic computation. This paper describes Boolean circuits (of bounded fan-in) for integer division (finding reciprocals) that have size
Parallel Algorithms for Shared-Memory Machines
  • R. Karp, V. Ramachandran
  • Computer Science
    Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity
  • 1990
Inversion of Triangular Toeplitz Matrices by Using the Fast Fourier Transform,
  • J. New Gener. Comput. Sys
  • 1989
The Art of Computer Programming: Seminumerical Algorithms
  • v. 2, Addison-Wesley, Mass.
  • 1981
Numerical and Algebraic Computations with Matrices and Polynomials , Vols. 1 and 2
  • Numerical and Algebraic Computations with Matrices and Polynomials , Vols. 1 and 2
  • 1992
...
...