ISSAC
2007
Springer
14 years 3 months ago
2007
Springer
Given a lattice basis of n vectors in Zn, we propose an algorithm using 12n3 + O(n2) floating point operations for checking whether the basis is LLL-reduced. If the basis is redu...
ISSAC
2007
Springer
14 years 3 months ago
2007
Springer
Approximate symbolic computation problems can be formulated as constrained or unconstrained optimization problems, for example: GCD [3, 8, 12, 13, 23], factorization [5, 10], and ...
ISSAC
2007
Springer
14 years 3 months ago
2007
Springer
Algebraic randomization techniques can be applied to hybrid symbolic-numeric algorithms. Here we consider the problem of interpolating a sparse rational function from noisy values...
ISSAC
2007
Springer
14 years 3 months ago
2007
Springer
Numerical homotopy continuation gives a powerful tool for the applied scientist who seeks solutions to a system of polynomial equations. Techniques from numerical homotopy continu...
ISSAC
2007
Springer
14 years 3 months ago
2007
Springer
We report on a high-level categorical parallel framework, written in the Aldor language, to support high-performance computer algebra on symmetric multi-processors and multicore p...
ISSAC
2007
Springer
14 years 3 months ago
2007
Springer
ISSAC
2007
Springer
14 years 3 months ago
2007
Springer
A new randomized algorithm is presented for computing the characteristic polynomial of an n × n matrix over a field. Over a sufficiently large field the asymptotic expected com...
ISSAC
2007
Springer
14 years 3 months ago
2007
Springer
We study arithmetic operations for triangular families of polynomials, concentrating on multiplication in dimension zero. By a suitable extension of fast univariate Euclidean divi...
ISSAC
2007
Springer
14 years 3 months ago
2007
Springer
Shirayanagi and Sweedler proved that a large class of algorithms over the reals can be modified slightly so that they also work correctly on fixed-precision floating-point numb...
ISSAC
2007
Springer
14 years 3 months ago
2007
Springer