Lecture 13 : Randomized Least - squares Approximation in Practice , Cont .
نویسنده
چکیده
The basic idea is that rather than doing a QR decomposition of A, do a QR decomposition on ΠA, where Π is a FJLT (or some other, e.g., data-aware subspace embedding), and then use the R̃−1 from QR on the subproblem as a preconditioner for an iterative algorithm on the original problem. We saw that if ΠA = Q̃R̃ then κ ( AR̃−1 ) = κ (SU). If we sample “enough,” i.e., Ω (d log(d)/ ), then this condition number is ≤ 1 + and the very good subspace embedding provides a very good preconditioner.
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