منابع مشابه
A polynomial-based division algorithm
A polynomial-based division algorithm and a corresponding hardware structure are proposed. The proposed algorithm is shown to be competitive to other conventional algorithms like the Newton-Raphson algorithm for up to about 32 bits accuracy. For example, using Newton-Raphson with less than 12 bits accuracy of the initial approximation, requires 33% more general multiplications than the proposed...
متن کاملPolynomial division and its computational complexity
(i) First we show that all the known algorithms for polynomial division can be represented as algorithms for triangular Toeplitz matrix inversion. In spite of the apparent difference of the algorithms of these two classes, their strong equivalence is demonstrated. (ii) Then we accelerate parallel division of two polynomials with integer coefficients of degrees at most m by a factor of log m com...
متن کاملSparse polynomial division using a heap
In 1974, Johnson showed how to multiply and divide sparse polynomials using a binary heap. This paper introduces a new algorithm that uses a heap to divide with the same complexity as multiplication. It is a fraction-free method that also reduces the number of integer operations for divisions of polynomials with integer coefficients over the rationals. Heap-based algorithms use very little memo...
متن کاملPolynomial multiplication and division using heap
We report on new code for sparse multivariate polynomial multiplication and division that we have recently integrated into Maple as part of our MITACS project at Simon Fraser University. Our goal was to try to beat Magma which is widely viewed in the computer algebra community as having state-of-the-art polynomial algebra. Here we give benchmarks comparing our implementation for multiplication ...
متن کاملImproved 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)
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ژورنال
عنوان ژورنال: IOSR Journal of Engineering
سال: 2012
ISSN: 2278-8719,2250-3021
DOI: 10.9790/3021-021051316