AI 中文总结
研究计算矩阵伪逆的直接方法，克服现有方法在揭示秩、条件数等方面的限制，通过重新解释现有方法及引入新变体，使其适用于大规模或稀疏多线性回归应用。
AI 中文摘要
矩阵的摩尔 - 彭罗斯伪逆可通过其奇异值分解来定义和计算。也存在计算矩阵伪逆的直接方法（即避免特征值计算的方法），但在实际中这些方法往往存在揭示秩、条件数不佳或其他限制。本文证明直接方法可克服这些限制，重新解释了几种现有直接方法并引入适用于大规模或稀疏多线性回归应用的新变体。
英文摘要
The Moore-Penrose pseudoinverse of a matrix can be defined and calculated using its singular value decomposition. There are also direct methods for computing matrix pseudo-inverses (those that avoid eigenvalue computations), but these are often rank-revealing, poorly conditioned, or otherwise limited in practice. In this paper, we demonstrate that direct methods can overcome these limitations. In particular, we reinterpret several existing direct methods and introduce new variations that are appropriate for large scale or sparse multilinear regression applications.
