数值分析课程中三次样条插值的教学探讨

摘要

Cubic Spline interpolation is widely applied in the engineering for its good smoothness. Also, cubic spline interpolation is treated as one important and tough section in the teaching and learning,since its definition is complicated and the difficulty to solve the interpolation functions. In order to make the students understand cubic spline interpolation more easily and solve practical problems with the spline interpolation skillfully, the teaching process can be undertaken through the following four steps. Firstly, inspires students to think and interests them by instance;secondly,introduces the concept of the spline interpolation;thirdly, solve cubic spline interpo-lation theoretically;finally, actualize cubic spline interpolation by Matlab.%三次样条插值由于良好的光滑性而在工程中应用非常广泛，同时又由于它的定义复杂、插值函数难于求解，使得三次样条插值成为教学中的重点和难点。为了使学生更加容易理解三次样条插值的概念，并熟练运用三次样条插值解决实际问题，在教学中首先通过实例激发学生思考，引起学生的学习兴趣；然后引入三次样条插值的概念，并从理论上给出三次样条插值的求解方法；最后再应用Matlab实现三次样条插值。