🚀 go-pugleaf

YOu should probasbly examine the subspace iteration method (also known a block
iteration methods).   You can find a reference in Bathe, Finite Element
Procedures for Engineering Analysis.

You might also explor the Lanczos method, check out Golub and Van Loan.
-- 

Regards.
 
Don Rolph  a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263

Sorry for the followup to my folowup.  I just reread and caught your statement
about geenral matrices.  If you mean unsymetric I have saome unpublished work
which extends subspace iteration to the unsymetric case.  I can forward a sketch
of the details if you are interested.
-- 

Regards.
 
Don Rolph  a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263

In article <1993Jan21.091649@roper.mc.ti.com> a722756@roper.mc.ti.com (W. Donald Rolph) writes:
>
>Sorry for the followup to my folowup.  I just reread and caught your statement
>about geenral matrices.  If you mean unsymetric I have saome unpublished work
>which extends subspace iteration to the unsymetric case.  I can forward a sketch
>of the details if you are interested.
>-- 
>
>Regards.
> 
>Don Rolph  a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263

Actually a considerable amount of work has been done on subspace
iteration for non-Hermitian matrices over the years.  I am appending a
bibliography.  The program SRRIT mentioned there is available by
anonymous ftp from thales.cs.umd.edu in pub/srrit (the accompanying
tech report is in pub/reports).  The code is still being tested, and
we would appreciate comments from users.

Pete Stewart

\begin{thebibliography}{1}

\bibitem{bast:92}
Z.~Bai and G.~W. Stewart.
\newblock {SRRIT}\,---\,a {FORTRAN} subroutine to calculate the dominant
  invariant subspace of a nonsymmetric matrix.
\newblock Technical Report 2908, Department of Computer Science, University of
  Maryland, 1992.

\bibitem{baue:57}
F.~L. Bauer.
\newblock {Das Verfahren der Treppeniteration und verwandte Verfahren zur
  L\"osung algebraischer Eigenwertprobleme}.
\newblock {\em {Zeitschrift f\"ur angewandte Mathematik und Physik}},
  8:214--235, 1957.

\bibitem{clje:71}
M.~Clint and A.~Jennings.
\newblock A simultaneous iteration method for the unsymmetric eigenvalue
  problem.
\newblock {\em Journal of the Institute for Mathematics and Applications},
  8:111--121, 1971.

\bibitem{dusc:91}
I.~S. Duff and J.~A. Scott.
\newblock Computing selected eigenvalues of sparse unsymmetric matrices using
  subspace iteration.
\newblock Report RAL-91-056, Central Computing Department, Rutherford Appleton
  Laboratory, 1991.

\bibitem{govl:89}
G.~H. Golub and C.~F. Van~Loan.
\newblock {\em Matrix Computations}.
\newblock Johns Hopkins University Press, Baltimore, Maryland, 2nd edition,
  1989.

\bibitem{jest:75}
A.~Jennings and W.~J. Stewart.
\newblock Simultaneous iteration for partial eigensolution of real matrices.
\newblock {\em J. Inst. Math. Appl.}, 15:351--362, 1975.

\bibitem{stew:75b}
G.~W. Stewart.
\newblock Methods of simultaneous iteration for calculating eigenvectors of
  matrices.
\newblock In J.~H. Miller, editor, {\em Topics in Numerical Analysis {II}},
  pages 185--196. Academic Press, New York, 1975.
\newblock Cited in \cite{govl:89}.

\bibitem{stew:76}
G.~W. Stewart.
\newblock Simultaneous iteration for computing invariant subspaces of a
  non-{Hermitian} matrix.
\newblock {\em {\it Numerische Mathematik\/}}, 25:123--136, 1976.

\bibitem{stew:78}
G.~W. Stewart.
\newblock {SRRIT}\,---\,a {FORTRAN} subroutine to calculate the dominant
  invariant subspaces of a real matrix.
\newblock Technical Report TRR-514, University of Maryland, Department of
  Computer Science, 1978.

\end{thebibliography}