Eigensystem Realization Algorithm (ERA) is a data-driven approach for subspace system identification and is widely used in many areas of engineering. However, the computational cost of the ERA is dominated by a step that involves the singular value decomposition (SVD) of a large, dense matrix with block Hankel structure. This paper develops computationally efficient algorithms for reducing the computational cost of the SVD step by using randomized subspace iteration and exploiting the block Hankel structure of the matrix. We provide a detailed analysis of the error in the identified system matrices and the computational cost of the proposed algorithms. We demonstrate the accuracy and computational benefits of our algorithms on two test problems: the first involves a partial differential equation that models the cooling of steel rails, and the second is an application from power systems engineering.

中文翻译：

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使用随机 SVD 实现本征系统的高效算法

特征系统实现算法 (ERA) 是一种数据驱动的子空间系统识别方法，广泛应用于许多工程领域。然而，ERA 的计算成本主要由涉及具有块 Hankel 结构的大型密集矩阵的奇异值分解 (SVD) 的步骤决定。本文开发了计算效率高的算法，通过使用随机子空间迭代并利用矩阵的块 Hankel 结构来降低 SVD 步骤的计算成本。我们对识别的系统矩阵中的误差和所提出算法的计算成本进行了详细分析。我们证明了我们的算法在两个测试问题上的准确性和计算优势：第一个涉及模拟钢轨冷却的偏微分方程，