广义绝对值方程的区间算法  

An Interval Algorithm for Generalized Absolution Value Equations

作　　者：王爱祥 WANG Ai-xiang(School of Mathematics,China University of Mining and Technology,Xuzhou,Jiangsu 221008,China;School of Aeronautical and Mechanical Engineering,Changzhou Institute of Technology,Changzhou,Jiangsu 213032,China)

机构地区：[1]中国矿业大学数学学院,江苏徐州221008 [2]常州工学院航空与机械工程学院,江苏常州213032

出　　处：《石家庄学院学报》2022年第6期52-56,共5页Journal of Shijiazhuang University

基　　金：国家自然科学基金(72071202)。

摘　　要：研究了广义绝对值方程的求解问题.在特定条件下,得到含有广义绝对值方程准确解的初始区间,然后提出了一个能不断缩小含解区间的区间迭代算法.该算法能同步显示绝对值方程近似解和准确解的误差范围,并证明了算法的收敛性且收敛速度至少是线性的.为提高计算效率,利用点迭代来代替区间迭代,最后进行了数值实验.理论分析和数值结果均表明所提算法是有效的.The algorithm for the solution of generalized absolute value equation is proposed. Under a certain condition, the initial interval containing the exact solution of the generalized absolute value equation is obtained.Then an interval iterative algorithm is given which can continuously reduce the interval containing the solution. The algorithm can synchronously display the error range between approximate solution and accurate solution. The convergence of the algorithm is proved and the convergence speed is at least linear. The point iteration is used instead of interval iteration to improve the computational efficiency. Finally, numerical experiments are carried out. Theoretical analysis and numerical results show that the algorithm is effective.

关 键 词：绝对值方程 区间算子 区间算法 

分 类 号：O242.2[理学—计算数学]