On a recursive method including both CG and Burg's algorithms
On a recursive method including both CG and Burg's algorithms
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包含 CG 和 Burg 算法的递归方法
DOI：
10.1016/j.amc.2012.07.024
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发表时间：
2012
影响因子：
4
通讯作者：
Masaya Matsuura
中科院分区：
文献类型：
--
作者：
M. Hirao;M. Sawa;Y. Zhou;Yuzuru Inahama;Sho Matsumoto;Hayato Waki;Masaya Matsuura
共轭梯度法（CG）是求解线性方程组的重要算法之一。另一方面，布尔格算法是一种估计时间序列模型参数的算法。这两种算法分别在数值计算和时间序列分析领域非常流行。然而，鲜为人知的是，这些算法具有共同的数学结构。似乎没有多少研究人员熟悉这两种算法。因此，在本文中，我们回顾这些算法，看看它们是如何相互关联的。这导致了时间序列分析中的“反平稳性”概念。
The CG method (conjugate gradient method) is one of the most important and useful algorithms for the numerical solution of linear equations. On the other hand, Burg’s algorithm is an algorithm for estimating the parameters of time series models. Both algorithms are quite popular in the field of numerical calculation and time series analysis, respectively. It is less known, however, that these algorithms have a common mathematical structure. It seems that not so many researchers are familiar with both of these algorithms. Therefore, in this paper, we review these algorithms and see how they are related with each other. This leads to a notion of “anti-stationarity” in time series analysis.