ISSAC
2007
Springer
13 years 11 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
13 years 11 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
13 years 11 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
13 years 11 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
13 years 11 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
13 years 11 months ago
2007
Springer
ISSAC
2007
Springer
13 years 11 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
13 years 11 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
13 years 11 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
13 years 11 months ago
2007
Springer