基于区间分析的不等式自动证明  

AUTOMATIC INEQUALITY PROVING BASED ON INTERVAL ANALYSIS

作　　者：侯晓荣[1] 邵俊伟[1] 

机构地区：[1]电子科技大学自动化工程学院,成都611731

出　　处：《系统科学与数学》2010年第10期1351-1358,共8页Journal of Systems Science and Mathematical Sciences

基　　金：国家973重点基础研究发展规划项目(2004CB318000);国家自然科学基金(10571095;61074189)资助

摘　　要：提出了一种基于区间分析的不等式自动证明方法,这一方法可以处理类型较为一般的不等式,只需对应的函数具有所需的高阶连续可微性质,而传统的不等式自动证明方法一般仅处理代数类型,或可最终转化为代数类型的不等式.实际例子显示,该方法可以解决一些其他方法无法解决的问题.A method based on interval analysis to automatically prove inequalities is proposed.This method can be applied to more general types of inequalities,which only need to be continuously differentiable to required order,whereas traditional methods of automatic inequality proving generally process algebraic inequalities or inequalities that can be ultimately converted to algebraic types.Simulation examples show that this method can solve some difficult problems that other approaches can not tackle.

关 键 词：区间分析 不等式 自动证明 

分 类 号：O178[理学—数学]