CORR
2008
Springer
13 years 4 months 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
13 years 4 months 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
13 years 4 months 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
13 years 4 months 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
13 years 4 months 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
13 years 4 months 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
13 years 4 months 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
13 years 4 months 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
13 years 4 months 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
13 years 4 months 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...