Compact and Infinite-Order Error Analysis for Null-Space SVD Estimation
We study null-space estimation from a noisy matrix. For a simple left null space, we first derive an exact compact expression for the error of the smallest left singular vector. We then give an all-order series for the SVD vector and projector, followed by compact and consistently truncated series forms for the fixed-realization empirical risk and conditional population generalization risk. The recursion extends to a multiple-dimensional null space by following the complete invariant subspace. The convergence radius is not inferred from an error plot: it is computed independently from the nearest complex exceptional point that joins a retained eigenvalue branch to its complement. A reduce...
| Authors | Xin Li, Jonathan Cohen, Rami Puzis |
|---|---|
| Primary category | math.ST |
| Published | 31 August 2026 |
| Last updated at source | 31 August 2026 |
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