I have a matrix for which I know its QR decomposition: [itex]A = QR[/itex]. I want to estimate the largest and smallest singular values of [itex]A[/itex] ([itex]\sigma_1[/itex] and [itex]\sigma_n[/itex]) however in my application it is too expensive to compute the full SVD of [itex]A[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

Is it possible to estimate the largest/smallest singular values from the QR decomposition? The only result I've been able to find so far is

[tex]

\left| \prod_i r_{ii} \right| = \prod_i \sigma_i

[/tex]

where [itex]r_{ii}[/itex] are the diagonal entries of [itex]R[/itex]. I'm not sure if this implies that the singular values of [itex]R[/itex] are the same as the singular values of [itex]A[/itex]. If thats true, it might be possible and less expensive for my application to compute [itex]SVD(R)[/itex] rather than [itex]SVD(A)[/itex].

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# Estimating singular values from QR decomposition

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