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Matter Modeling

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  • $\begingroup$ +100. Thanks for writing such an excellent and thorough answer again! I also appreciate you staying up late to write it :) $\endgroup$ Commented Mar 17, 2022 at 2:39
  • $\begingroup$ @NikeDattani my pleasure & thanks for sorting out the numbering & references - I couldn't quite face that by the time I got to the end! $\endgroup$ Commented Mar 17, 2022 at 16:39
  • $\begingroup$ Instead of letting the average eigenvalue of $\alpha\mathrm{B}$ be 1, there are many seemingly equally justified way of choosing $\alpha$, for example one may let the average eigenvalue of $\alpha^{-1}\mathrm{B}^{-1}$ be 1, or essentially use the average eigenvalue of $\alpha^{n}\mathrm{B}^{n}$ for any non-zero $n$. The resulting $\alpha$ clearly depends on $n$ if $\mathrm{B}$ is not diagonal. Could you elaborate on the significance of choosing $n=1$ here? $\endgroup$ Commented Mar 20, 2022 at 11:35
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    $\begingroup$ @wzkchem5 I was trying not to stray too far into optimisation theory, but I'll try to add something at the end when I have time. It's actually more complicated, since the choice of 1 is "optimal" in the sense of reducing the mean error, but the whole argument is predicated on remaining in the quadratic well; if eigenvalues are large, you sometimes need a smaller alpha for stability, even though that brings the average below 1. $\endgroup$ Commented Mar 21, 2022 at 10:21