Earll,
> I apologize this is not directly Deal.ii related, but I wanted to share it in > case it contains something enlightening for deal.ii developers. > > A friend of mine in the physics community shared this article: > [...] > > My knowledge of eigenvector and eigenvalue calculation is very rusty, but I > understand they are claiming to have simplified eigenvector calculation under > certain conditions. Does anyone know what this means in a practical sense? Is > this clickbait? Does anyone understand this article well enough to say if it > has computational implications outside quantum mechanics? I'm no eigenvalue expert either, but it's an interesting formula. In general, if Terence Tao speaks, it's worth listening :-) As for practical impact, I think this comment is useful: https://terrytao.wordpress.com/2019/08/13/eigenvectors-from-eigenvalues/#comment-529043 But at least as far as the community on this mailing list is concerned, it's worth keeping in mind two issues: * The matrices we have are sparse; that makes a lot of things more complicated, but also some much easier. * The matrices for which we consider eigenvalues are generally finite-dimensional approximations of infinite-dimensional operators. That means that in general only the matrix eigenvalues at either the low or the high end of the spectrum are good approximations of the operator eigenvalues, and those are the ones we're generally interested in. In other words, we almost never compute all eigenvalues of a matrix because most of them are meaningless. So we only care about a few eigenvalues and corresponding eigenvectors (and have efficient Krylov space methods to compute them) -- but then a formula that requires us to know *all* eigenvalues of a matrix (plus all eigenvalues of all of the M matrices) is not going to be of great help to our community. Best W. -- ------------------------------------------------------------------------ Wolfgang Bangerth email: [email protected] www: http://www.math.colostate.edu/~bangerth/ -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/ea8ca439-4e61-d95e-1e20-1f9b0b783155%40colostate.edu.
