摘要
介绍了拉格朗日多项式插值和切比雪夫多项式拟合的原理,阐述了插值和拟合的滑动式算法。通过算例分析了插值法和拟合法的精度,研究了多项式阶数以及节点数对精度的影响。结果表明:在一定范围内,多项式的阶数越高,插值和拟合的精度越高。当切比雪夫多项式拟合节点数选为拟合阶数加上1时,拟合精度最高,其结果与拉格朗日插值结果有很高的一致性。
This paper introduces the theories of Lagrange interpolation and Chebyshev fitting, describes the sliding algorithm of interpolation and fitting. Then the accuracy of interpolation and fitting is analysed by examples, and the research on the influences of polynomial ranks and knots number is also done in the paper. The results showed that with a certain range, the higher the polynomial ranks, the more accurate the interpolation and fitting. The fitting accuracy achieves highest when the knots number of Chebyshev polynomial equals to the polynomial ranks plus one. In this case, the fitting results has a high consistency with Lagrange interpolation results.
出处
《全球定位系统》
2011年第2期40-44,共5页
Gnss World of China
关键词
精密星历
拉格朗日插值
切比雪夫拟合
精度
Precise ephemeris
Lagrange interpolation
Chebyshev fitting
accuracy
