Applications of interval arithmetic in solving polynomial equations by Wu's elimination method

Abstract

Wu's elimination method is an important method for solving multivariate polynomial equations. In this paper, we apply interval arithmetic to Wu's method and convert the problem of solving polynomial equations into that of solving interval polynomial equations. Parallel results such as zero-decomposition theorem are obtained for interval polynomial equations. The advantages of the new approach are two-folds: First, the problem of the numerical instability arisen from floating-point arithmetic is largely overcome. Second, the low efficiency of the algorithm caused by large intermediate coefficients introduced by exact compaction is dramatically improved. Some examples are provided to illustrate the effectiveness of the proposed algorithm.