Sensitivity of low-rank matrix recovery
نویسندگان
چکیده
We characterize the first-order sensitivity of approximately recovering a low-rank matrix from linear measurements, standard problem in compressed sensing. A special case covered by our analysis is approximating an incomplete matrix. This one customary approach to build recommender systems. give algorithm for computing associated condition number and demonstrate experimentally how measurements affects it. In addition, we study best rank-r approximation problem. It measures Frobenius norm much infinitesimal perturbation arbitrary input amplified movement its approximation. explicit formula number, which shows that it depends on relative singular value gap between rth $$(r+1)$$ th values
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ژورنال
عنوان ژورنال: Numerische Mathematik
سال: 2022
ISSN: ['0945-3245', '0029-599X']
DOI: https://doi.org/10.1007/s00211-022-01327-7