函数分段有理二次Bézier插值与逼近

The Segment Rational Quadratic Bézier Interpolation and Approximation to Functions

依据几何特征对函数进行合理分段,定义了函数的分段三角形凸包,给出了控制多边形的确定方案,详细地讨论了函数的分段有理二次Bézier插值算法.定义了一种便于计算的新型误差,在此误差意义之下,插值算法的精度高于已有的逼近算法.数值实验结果表明了算法的可行性和有效性.

Based on the proper segmentation of non-linear functions, the triangle convex hull of function segments is given. A scheme of control polygon determination by the tangent of the endpoints of the segment intervals is provided. The algorithm of segment rational quadratic Bézier interpolation of non-linear functions is discussed in details. Moreover, a new kind of error is defined so as to simplify the computation. In the sense of the new definition of error, the precision of the interpolation algorithm is better than that of traditional approximate one, and the feasibility and validity of the algorithm is demonstrated by the numerical experiment.