🚀 go-pugleaf

In article <28OCT199212582520@rigel.tamu.edu>, i0c0256@rigel.tamu.edu (IGOR) writes:
|> In article <1992Oct28.041326.9273@marlin.jcu.edu.au>, maawg@marlin.jcu.edu.au (Andrew Gill) writes...
|> >Subject: Finding Largest Imag Part Complex Eigenvalue
|> >[stuff deleted]
|> >Im solving some hydrodynamic stability problems numerically and wind up
|> >needing to find the complex eigenvalue which has the largest imaginary 
|> >part, of a possibly complex matrix.
|> > 
|> >Currently I am using the QR
|> >algorithm (IMSL) which solves for all eigenvalues and is kind of time
|> >consuming (wasting?) when my matrices are around 200 or 300 big. 
|> > 
|> >Are there routines which can find just that *one* eigenvalue with the
|> >largest imaginary part?  I had hoped to stay away from methods requiring
|> 
|> Yes it seems there is one, As Dr K.P Chen fro  Arizona State University
|> pointed out to me, it seems that the method you are refering to is 
|> called the Arnoldi scheme, I searched for some references and found
|> in a siam paper that this method was perfected by some french
|> people at IBM in Paris.
|> [stuff deleted]

I've been using Arnoldi & other techniques on large non-symmetric matrices from
continuous-time Markov chains of size 10^4 and larger.
Arnoldi is good, but there are other things you might like to know about, such
as some ideas in

Large scale eigenvalue problems : proceedings of the IBM Europe Institute on
          Large Scale Eigenvalue Problems held in Oberlech, Austria, July 8-12,
          1985. 1986. IBM Europe Institute on Large Scale Eigenvalue Problems
	  edited by Jane Cullum and Ralph A. Willoughby
	  published by North-Holland (1986).

If you look through journals I'm sure you could find more stuff.
There is also

	"Chebyshev acceleration techniques for solving nonsymmetric eigenvalue
problems" by Y. Saad, Math. Comp. v.42, pp.567--588 (1984)

&	"Arnoldi-Tchebychev procedure for large-scale nonsymmetric matrices" by
D. Ho, F. Chatelin and M. Bennani, Mod'elisation Math'ematiques et Analyse
Num'erique v.24, pp.53--65 (1990)

and an early paper co-authored by Y. Saad.
------------------------------------------------------------------------
David Stewart			Program in Advanced Computation
des@thrain.anu.edu.au		School of Mathematical Sciences
				Australian National University
------------------------------------------------------------------------
David Stewart			Program in Advanced Computation
des@thrain.anu.edu.au		School of Mathematical Sciences
				Australian National University