Aitken迭代Delta^2过程、Wynn迭代算法和Brezinski迭代Theta算法的预测性质
Prediction Properties of Aitken's Iterated Delta^2 Process, of Wynn's Epsilon Algorithm, and of Brezinski's Iterated Theta Algorithm
摘要：
分析了幂级数序列的Aitken迭代Delta^2过程、Wynn迭代算法和Brezinski迭代theta算法的预测性质。作为第一步，这些变换的定义递归计划进行了适当的重新安排，以允许推导精度通过顺序的关系。在此基础上，有理逼近式可改写为一个部分和加上适当的变换项。这种变换项是一个有理函数，可以递归计算，它的泰勒展开式产生了（形式）幂级数的那些系数的预测，这些系数没有用于计算相应的有理逼近。
英文摘要：
The prediction properties of Aitken's iterated Delta^2 process, Wynn's epsilon algorithm, and Brezinski's iterated theta algorithm for (formal) power series are analyzed. As a first step, the defining recursive schemes of these transformations are suitably rearranged in order to permit the derivation of accuracy-through-order relationships. On the basis of these relationships, the rational approximants can be rewritten as a partial sum plus an appropriate transformation term. A Taylor expansion of such a transformation term, which is a rational function and which can be computed recursively, produces the predictions for those coefficients of the (formal) power series which were not used for the computation of the corresponding rational approximant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
