Parallel algorithms for matrix polynomial division

Isomorphic New Parallel Division Methods and Parallel Algorithms for Giant Matrix Transpose

In this paper, the weakness of the traditional matrix division methods for giant matrix transpose is pointed; Specific to the nature of the giant matrixes’ transpose and based on the characteristics of asynchronous PRAM parallel computing model, some new division (such as booklet belt division, closed-loop division and Checkerboard-belt-shaped compound division) methods are proposed for improvi...

Isomorphic New Parallel Division Methods and Parallel Algorithms for Giant Matrix Transpose

In this paper, the weakness of the traditional matrix division methods for giant matrix transpose is pointed; Specific to the nature of the giant matrixes’ transpose and based on the characteristics of asynchronous PRAM parallel computing model, some new division (such as booklet belt division, closed-loop division and Checkerboard-belt-shaped compound division) methods are proposed for improvi...

Improved Parallel Polynomial Division and Its Extensions

We compute the rst N coeecients of the reciprocal r(x) of a given polynomial p(x), (r(x)p(x) = 1 mod x N , p(0) 6 = 0), by using, under the PRAM arithmetic models , O(h log N) time-steps and O((N=h)(1 + 2 ?h log (h) N)) processors, for any h, h = 1; 2; : : : ; log N, provided that O(log m) steps and m processors suuce to perform DFT on m points and that log (0)

Fast Parallel Algorithms for Polynomial Division over an Arbitrary Field of Constants

Al~tract--It is shown that the division of an m th-degree polynomial by an n th-degree.polynomial can be performed over an arbitrary field of constants F involving O( log (m-n + I)log log(m n + 1)) parallel steps and a polynomial in m number of processors. If the field F has more than 2 + 2(m n + 1)rain{n, m n } distinct elements, then O(log(m n + I)) parallel steps and the polynomial number of...

Optimal Algorithms for Parallel Polynomial Evaluation