基于区间算术的多项式函数值域的简捷求法  

A Simple Method for Finding the Ranges of Polynomial Functions Based on Interval Arithmetic

作　　者：吕鑫 侯国亮 Lü Xin;HOU Guo-liang(School of Mathematics,Changchun Normal University,Changchun 130032,China)

机构地区：[1]长春师范大学数学学院,吉林长春130032

出　　处：《长春师范大学学报》2022年第10期1-5,共5页Journal of Changchun Normal University

基　　金：长春师范大学自然科学基金项目“区间分析应用研究”(2021003)。

摘　　要：研究了多项式函数值域的新求法.基于区间算术的初等理论,针对区间运算扩张的缺陷,运用多项式函数所特有的泰勒公式、秦九韶算法思想和其他控制区间运算扩张的有效措施,提出了计算多项式函数值域的简捷方法.相比于繁琐难懂的传统求法,通过具体实例证明了新方法简单易学.A new method for finding the range of polynomial function is studied. Based on the elementary theory of interval arithmetic, a simple method to evaluating the range of polynomial function is presented with its Taylor’s formula, the thought of Qin Jiushao algorithm and other effective techniques to control the overestimation of interval operations. Compared with the traditional methods, specific examples show that the new method is simple and easy to learn.

关 键 词：函数值域 区间算术 多项式函数 秦九韶算法 泰勒中值定理 

分 类 号：O242.29[理学—计算数学]