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short compilation:fractional iteration-> eigendecomposition
bo198214 Wrote:I just skimmed through and agree that some part should go into the FAQ.
I like the illustration by examples.
Though I find the V(x)~ very cumbersome ...
... this is Pari/GP... In my own matrix-calculator I implemented ' for transpose - but this is again misleading in a context of discussion of derivatives. What I really *hate* is the T-superscript Sad . So any good proposal is welcome...
Quote:Perhaps also the "Identities with binomials,Bernoulli- and other numbertheoretical numbers" at the bottom of the pages should be updated Wink
Quote:What I miss however is a suitable discussion of finite versus infinite matrices. For example if you approximate an infinite matrix M by finite matrices M_n then the inverse of the infinite matrix is not always the limit of the inverses of M_n.

Which is discussed in this video (unfortunately it seems currently not to be available) which I mentioned already here.

Well, it's a bit time ago, that I found small books concerning that matter and going into it in at least some detail. In general, I felt lost with that subject - may be I missed better treatises because I didn't recognize them - if the surrounding jungle of abstract terms/formalisms etc is too wild.
I really liked it, if I found something straightforward... In this view, the video was not helpful for me - not only was it very generally discussed beginning with infinite matrices to both sides, also I didn't find relations to my real problems with them (maybe I only was unable to see this): beginning with triangular real matrices, proceeding to complex-valued matrices and then, possibly, extension to fourway-infinite matrices. And including the concept of divergent series: I think it is needed to be familiar with this, since in our context we have to deal with such matrices/powerseries daily.

Gottfried Helms, Kassel

Messages In This Thread
RE: short compilation:fractional iteration-> eigendecomposition - by Gottfried - 01/19/2008, 02:29 PM

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