Accurate Downdating of Least Squares Solutions
Accurate Downdating of Least Squares Solutions
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DOI：
10.1137/s089547989222895x
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发表时间：
1994-04
期刊：
影响因子：
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通讯作者：
Å. Björck;Haesun Park;L. Eldén
中科院分区：
文献类型：
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作者：
Å. Björck;Haesun Park;L. Eldén
在许多应用中，需要对一系列修改的最小二乘问题的解决方案，其中要么添加新的观测值（更新），要么删除旧的观测值（更新）。如果数据矩阵的完全QR分解是可用的，则可以构造用于向下更新的稳定算法。只向下更新$R $而不存储$Q $的算法需要较少的操作。然而，它们不能提供良好的准确性，并且在病态问题发生后可能无法恢复准确性。作者描述了一种新的算法，准确的最小二乘解决方案，并将其与现有的算法进行比较。数值试验结果也提出了使用滑动窗口方法，其中一些更新和downdatings重复发生。
Solutions to a sequence of modified least squares problems, where either a new observation is added (updating) or an old observation is deleted (downdating), are required in many applications. Stable algorithms for downdating can be constructed if the complete QR factorization of the data matrix is available. Algorithms that only downdate $R$ and do not store $Q$ require less operations. However, they do not give good accuracy and may not recover accuracy after an ill-conditioned problem has occurred. The authors describe a new algorithm for accurate downdating of least squares solutions and compare it to existing algorithms. Numerical test results are also presented using the sliding window method, where a number of updatings and downdatings occur repeatedly.