Smoothed Analysis of Moore-Penrose Inversion
arXiv:1002.469023 citationsh-index: 36
Originality Incremental advance
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Provides theoretical guarantees for numerical stability of Moore-Penrose inversion in machine learning and scientific computing.
The paper performs a smoothed analysis of the condition number of rectangular matrices, proving that its expected value asymptotically depends only on matrix elongation, not on distribution center or variance.
We perform a smoothed analysis of the condition number of rectangular matrices. We prove that, asymptotically, the expected value of this condition number depends only of the elongation of the matrix, and not on the center and variance of the underlying probability distribution.