中文摘要：

在数值分析的许多领域中,许多方法都是借助于插值公式导出的。几乎所有的经典数值微分、数值求积和常微分方程的数值积分公式都可以从插值公式推导出来。分形插值方法是近几十年发展起来的一种局部非线性插值方法,它提供了拟合实验数据的一种新方法。在分形插值方法中,垂直比例因子是影响插值精度的主要因素。在实验的基础上给出了垂直比例因子的局部显式表达式。通过比较固定比例因子和变化比例因子分形插值的精度,说明了显式垂直比例因子分形插值方法的高精度和高效率。

英文摘要：

Interpolation formulas are the starting points in the derivations of many methods in several areas of Numerical Analysis. Almost all the classical methods of numerical differentiation, numerical quadrature and numerical integration of ordinary differential equations are directly derivable from interpolation formulas. Fractal interpolation method that is a locally nonlinear interpolation method developed in recent years provides a new means for fitting experimental data. The vertical scaling factor is an important parameter in the application of fractal interpolation method, which meanly decides the accuracy of the interpolation. The locally explicit expression of the vertical scaling factor is presented on the basis of numerical experiments. The numerical experiments of fixed and variational vertical scaling factors demonstrate that the fractal interpolation method using explicit expression of the vertical scaling factor has high accuracy and efficiency.