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In this paper, we present perturbation analysis and randomized algorithms forthe total least squares (TLS) problems. We derive the perturbation bound andcheck its sharpness by numerical experiments. Motivated by the recently popularprobabilistic algorithms for low-rank approximations, we develop randomizedalgorithms for the TLS and the truncated total least squares (TTLS) solutionsof large-scale discrete ill-posed problems, which can greatly reduce thecomputational time and still keep good accuracy.

Perturbation Analysis and Randomized Algorithms for Large-Scale Total Least Squares Problems