Padé approximation of Stieltjes series
Padé approximation of Stieltjes series
复制标题
Stieltjes 级数的 Padé 近似
DOI：
10.1016/0021-9045(75)90077-5
复制
发表时间：
1975
影响因子：
0.9
通讯作者：
Philip Smith
中科院分区：
文献类型：
--
作者：
G. Allen;C. Chui;W. Madych;F. Narcowich;Philip Smith
利用[n，n−1]Pad‘e逼近的Nutall紧致公式，证明了Stieltjes级数的Padé逼近与正交多项式之间存在着天然的联系。特别地，我们得到了精确的误差公式。这种情况下的[n，n−1]Padé逼近是Stieltjes积分的高斯求积。因此，误差分析现在是可能的，并且在非常温和的条件下证明了[n，n+j]，j⩾−1，Padé逼近收敛于Stieltjes积分。
Using Nuttall's compact formula for the [n,n− 1] Pad'e approximant, the authors show that there is a natural connection between the Padé approximants of a series of Stieltjes and orthogonal polynomials. In particular, we obtain the precise error formulas. The [n,n− 1] Padé approximant in this case is just a Gaussian quadrature of the Stieltjes integral. Hence, analysis of the error is now possible and under very mild conditions it is shown that the [n,n+j],j⩾ − 1, Padé approximants converge to the Stieltjes integral.