中心形式的区间自动微分

Centred form interval automatic differentiation

自动微分是用于计算多变量函数的导数和偏导数的一种微分技术,在给定一个多变量光滑函数值的程序代码后,可以很容易地利用自动微分来实现有关导数和偏导数的精确计算.中心形式的区间算术是一种估计多项式函数取值范围的有效方法.文章将自动微分技术与中心形式的区间算术相结合应用到计算机图形学领域隐式函数曲线绘制的细分算法中,并与以往的几种隐式曲线绘制方法作比较和分析,实验数据表明中心形式的区间自动微分在绘制隐式曲线方面更精确.

Automatic differentiation is a technique to evaluate the derivatives of a function defined by a computer program.Given the program code of a multivariate smooth function,we can easily use automatic differentiation to calculate its derivative and partial derivative accurately.The centred form interval arithmetic is an effective method to estimate the range of a polynomial function.Automatic differentiation technique and centred form interval arithmetic are combined and applied to the subdivision based implicit curve plotting algorithm in this paper.A comparison of this new method with several other methods is conducted which shows that the centred form interval automatic differentiation is more precise.