The Krylov subspace method has been investigated and refined for approximating the behaviors of finite or infinite dimensional linear operators. It has been used for approximating eigenvalues, solutions of linear equations, and operator functions acting on vectors. Recently, for time-series data analysis, much attention is being paid to the Krylov subspace method as a viable method for estimating the multiplications of a vector by an unknown linear operator referred to as a transfer operator. In this paper, we investigate a convergence analysis for Krylov subspace methods for estimating operator-vector multiplications.

中文翻译：

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希尔伯特空间中估计算子矢量乘法的Krylov子空间方法

已经对Krylov子空间方法进行了研究和改进，以近似有限或无限维线性算子的行为。它已用于近似特征值，线性方程的解以及作用于矢量的算子函数。近来，对于时间序列数据分析，作为一种可行的方法，Krylov子空间方法引起了人们的极大关注，该方法用于估计由未知线性算子（称为传递算子）进行的向量乘法。在本文中，我们研究了Krylov子空间方法的收敛性分析，用于估计算子矢量乘法。