Probabilistic algorithms for polynomial absolute factorization

C. Bertone, G. Chéze, A. Galligo
2010 ACM SIGSAM Bulletin  
We show a fast algorithm to find a rational number in a given real interval whose denominator is minimal. The algorithm is similar to the regular continued fraction expansion for a real number. Abstract We provide a method of determining whether there exist some p ∈ P and f ∈ F such that p is divisible by f for a pair of real multivariate interval polynomials, P and F . Although this problem is written as a feasibility problem for a system of nonlinear algebraic equations, it is an NP-hard
more » ... em and is thus difficult to solve. Our approach is iterative based on interval analyses, which outputs the regions containing the solutions if the system is feasible; otherwise, it outputs the fact of infeasibility. We also propose two methods for where the system of algebraic equations is underdetermined, the first obtains the regions that enclose all solutions, and the second obtains the solution that minimizes error in the Euclidean norm.
doi:10.1145/1823931.1823936 fatcat:paopikhxnzao7ez5vjkcp6gi3y