Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
On real factors of real interval polynomials
Journal of Symbolic Computation
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We provide a method of determining whether there exist some p 2 P and f 2 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 problem 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.