Krylov Subspace Estimation
Krylov Subspace Estimation
复制标题
Krylov子空间估计
DOI：
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复制
发表时间：
2000
影响因子：
3.1
通讯作者：
A. Willsky
中科院分区：
文献类型：
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作者：
M. Schneider;A. Willsky
在给定噪声数据的情况下，计算高维随机量的线性最小二乘估计需要求解大型线性方程组。在许多情况下，可以使用Krylov子空间方法有效地求解该系统，例如共轭梯度（CG）算法。计算估计误差方差是一项更复杂的任务。这是困难的，因为误差方差是涉及给定矩阵的逆的矩阵表达式的对角元素。本文提出了一种利用CG算法产生的共轭搜索方向来获得估计误差方差的收敛逼近的方法。用于计算误差方差福尔斯的算法自然地从CG算法的新的估计理论解释中消失。本文讨论了这种解释和收敛性问题，并给出了数值例子。这些例子包括海洋学中的105维估计问题。
Computing the linear least-squares estimate of a high-dimensional random quantity given noisy data requires solving a large system of linear equations. In many situations, one can solve this system efficiently using a Krylov subspace method, such as the conjugate gradient (CG) algorithm. Computing the estimation error variances is a more intricate task. It is difficult because the error variances are the diagonal elements of a matrix expression involving the inverse of a given matrix. This paper presents a method for using the conjugate search directions generated by the CG algorithm to obtain a convergent approximation to the estimation error variances. The algorithm for computing the error variances falls out naturally from a new estimation-theoretic interpretation of the CG algorithm. This paper discusses this interpretation and convergence issues and presents numerical examples. The examples include a 105-dimensional estimation problem from oceanography.