SVDRANDOMIZED

SVDRANDOMIZED = “randomized” - A basic randomization-based singular value solver.

Notes

Only available for standard SVD problems.

This solver relies on randomization techniques described in [Halko et al., 2011]. It is different from other solvers in the sense that it assumes that the input matrix has low rank, in which case the computation will be very fast. Otherwise, the solver will proceed iteratively as a subspace iteration solver (which may have slow convergence), until the required accuracy is reached. Alternatively, it is possible to set a limited number of iterations (e.g., 1) and the solver will return approximate bases of the dominant singular spaces. Note that in this latter case, the individual singular vectors are not good approximations, so residuals are expected to be large.

References

[Hal11]

N. Halko, P. G. Martinsson, and J. A. Tropp. Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. SIAM Rev., 53(2):217–288, 2011. doi:10.1137/090771806.

See Also

SVD: Singular Value Decomposition, Mathematical Background, SVD, SVDType, SVDSetType(), SVDSetProblemType(), SVDTRLANCZOS

Level

beginner

Location

src/svd/impls/randomized/rsvd.c

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