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

作     者：CHEN Falai & YANG Wu Department of Mathematics,University of Science and Technology of China,Hefei 230026,China 

出 版 物：《Science China Mathematics》 (中国科学:数学(英文版))

年 卷 期：2005年第9期

页      面：110-123页

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

主　　题：mathematical mechanization Wu’s method polynomial equation interval arithmetic 

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