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Numerical algorithms for problems in analysis and algebra, scientific computation

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Shifted QR algorithm—why does the shift help?

As explained in Answer 3, the shift can be explained by the inverse power iteration. $x'=(A-rI)^{-1}x$ has larger component in $v_1$ if $r$ is closer to $\lambda_1$. However in QR iteration, we don't …
Tongru Huo's user avatar