On 11/20/19 9:53 PM, Earl Fairall wrote: > > You successfully answered all my questions; however, you now have me curious > why the physics community would want to know all (or a larger portion of) the > eigenvalues. If they're using these methods to somehow characterize the wide > frequency range of light or radiation, I can imagine that would get nasty > very > quickly!
In the context of the calculations that these people cared about, their matrices were 3x3 or 8x8 or something similarly small. Their matrices are not finite-dimensional approximations of infinite-dimensional operators, and so the eigenvalues have physical reality. On the other hand, in the finite element context, our matrices are approximations of infinite-dimensional operators, and so only those matrix eigenvalues that approximate operator eigenvalues well have physical relevance -- these are generally the first few (dozens, hundreds) smallest or largest eigenvalues of a matrix. 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/44c53861-3a9e-c438-e108-45feb63afda3%40colostate.edu.
