CORR
2008
Springer
14 years 16 days ago
2008
Springer
We present algorithms to perform modular polynomial multiplication or modular dot product efficiently in a single machine word. We pack polynomials into integers and perform sever...
CORR
2010
Springer
14 years 16 days ago
2010
Springer
Smale's -theory uses estimates related to the convergence of Newton's method to give criteria implying that Newton iterations will converge quadratically to solutions to ...
CORR
2010
Springer
14 years 16 days ago
2010
Springer
We consider the problem of isolating the real roots of a square-free polynomial with integer coefficients using (variants of) the continued fraction algorithm (CF). We introduce a...
CORR
2010
Springer
14 years 16 days ago
2010
Springer
In this paper we study planar polynomial differential systems of this form: dX dt = X = A(X, Y ), dY dt = Y = B(X, Y ), where A, B Z[X, Y ] and deg A d, deg B d, A H and B H. ...
CORR
2010
Springer
14 years 16 days ago
2010
Springer
In a recent paper Lima, Panario and Wang have provided a new method to multiply polynomials in Chebyshev basis which aims at reducing the total number of multiplication when polyn...
CORR
2008
Springer
14 years 16 days ago
2008
Springer
We study the problem of factoring univariate polynomials over finite fields. Under the assumption of the Extended Riemann Hypothesis (ERH), Gao [Gao01] designed a polynomial time ...
CORR
2010
Springer
14 years 16 days ago
2010
Springer
In their paper on the "chasm at depth four", Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of size 2o(m) al...
CORR
2010
Springer
14 years 16 days ago
2010
Springer
Abstract--The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoreti...
CORR
2010
Springer
14 years 16 days ago
2010
Springer
Finding the product of two polynomials is an essential and basic problem in computer algebra. While most previous results have focused on the worst-case complexity, we instead emp...
CAGD
2008
14 years 16 days ago
2008
A plane algebraic curve can be represented as the zero-set of a polynomial in two - or if one takes homogenous coordinates: three - variables. The coefficients of the polynomial de...