基于区间牛顿法的点到参数曲线最小距离的计算方法

作者：钱春 日期：2010-03-26/span> 浏览：3821 查看PDF文档

基于区间牛顿法的点到参数曲线最小距离的计算方法

钱春
（浙江工商大学 统计与数学学院，浙江 杭州 310018）

摘要：求解点到参数曲线的最小距离常常用一般的搜索算法。针对搜索算法的稳定性和有效性通常不高的问题，基于参数曲线的几何特性，将求最小距离转化为方程求解问题，应用了区间牛顿法来求解方程。研究结果表明，区间牛顿法是一个全局收敛的方程求根算法，具有较高的稳定性。
关键词：参数曲线；最小距离；区间算术；区间牛顿法
中图分类号：TP391.72文献标识码：A文章编号：1001-4551(2010)01-0082-03

Computing method for the minimum distance from a point to a parametric curve
based on the interval Newton method
QIAN Chun
(School of Statistics & Applied Mathemetics, Zhejiang Gongshang University, Hangzhou 310018, China)
Abstract: Searching algorithm is popularly used for solving the problem how to compute the minimum distance from a point to a parametric curve. Aiming at the poor stability and the low efficiency of the searching algorithm, based on the geometric characteristics of the parametric curve, the problem of finding the minimum value was changed into the problem of finding roots of an equation. Interval Newton method was adopted to solve the equation. The results indicate that Interval Newton method is a global convergence algorithm, and it is very stable.
Key words: parametric curve; minimum distance; interval arithmetic; interval Newton method
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