A Fast Randomized Algorithm for computing the Null Space

@article{Nakatsukasa2022AFR,
  title={A Fast Randomized Algorithm for computing the Null Space},
  author={Yuji Nakatsukasa and Taejung Park},
  journal={ArXiv},
  year={2022},
  volume={abs/2206.00975}
}
Randomized algorithms in numerical linear algebra can be fast, scalable and robust. This paper examines the effect of sketching on the right singular vectors corresponding to the smallest singular values of a tall-skinny matrix. We devise a fast algorithm for finding the trailing right singular vectors using randomization and examine the quality of the solution using multiplicative perturbation theory. For an m × n ( m ≥ n ) matrix, the algorithm runs with complexity O ( mn log n + n 3 ) which is… 

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Local operator theory, random matrices and Springer Nature 2021 LTEX template A Fast Randomized Algorithm for computing the Null Space 25 Banach spaces

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