牛顿方法的用导一致性

导数及其使用是一种重要的数学工具与方法,在数值方法研究中起着十分重要的作用,很多经典数值计算方法理论中都涉及了对导数的运用.作为常用的数值方法,牛顿方法大量利用了求导的思想.通过归纳牛顿迭代法的显性用导特性和牛顿插值多项式的隐性用导特性,得到牛顿方法的用导一致性.

Consistency of Derivative Exploitation in Newton Methods

Derivatives and their use as an important mathematical tool and method plays an important role in the research of numerical methods. In addition, many classical numerical methods involve the use of derivatives. Being commonly-used ,Newton methods exploit the idea of using derivatives extensively. By summing up the explicit use of derivatives in Newton iteration method and the implicit use of derivatives in Newton interpolation polynomial, the consistency of using derivatives in Newton methods is thus illustrated.