带有扰动的Chebyshev-Padé逼近

Perturbed Chebyshev-Padé approximation

提出了一种新的带有扰动的Chebyshev-Padé逼近,它依赖于一个扰动参数,其优点在于:它可以通过调整扰动参数来提高逼近的精度。给出了带有扰动的Chebyshev-Padé逼近的计算表达式;讨论了函数f(x)的导数及其原函数F(x)的带有扰动的Chebyshev-Padé逼近.通过时间复杂度分析,说明了在大致相同的精度下,文章方法较之经典的Chebyshev-Padé逼近所需的计算量要少得多;最后,以具体的数值例子说明这种新方法的优越性。

A novel kind of perturbed Chebyshev-Padé approximation based on a perturbation parameter is derived. The merit of this kind of perturbed Chebyshev-Padé approximation is that by adjusting the perturbation parameter, a higher degree of approximation can be obtained. The method of calculating the perturbed Chebyshev-Pad6 approximation is proposed for not only the general situation but also some special cases, i. e. , an odd function and an even one. The novel approximation formulas for the derivatives off（x） and the original functions are also discussed. By the time-complexity analysis, it is illustrated that compared with the traditional Chebyshev-Padé approximation, the novel approximation presented in this paper calls for less calculation with almost the same accuracy. Finally, some numerical examples are given to show the advantages of the novel approximation over the traditional method.