# Summary: algorithm for eigenvalues

*From*: nila'
at \`solidmr.kun.nl (Niels van der Laag)
*Subject*: Summary: algorithm for eigenvalues
*Date*: Fri, 1 Nov 1996 10:49:19 +0100

Dear CCL-ers,
Last week I posted a question about eigenvalaues of a large
banded hermitian matrices. I got several responses which I
summarized here below.
The best way to do this is to use the Householder reduction and
after that an QR method. With all the answers I recieved,I will
try to modify the algorithm so it would fit strictly to my problem.
For theoretical explenation:
Wilkinson, "The Algebraic Eigenvalue Problem", Clarendon Press, Oxford
(1965)
(there should be a newer edition, but I didn't find it in our library)
Press et. al., Numerical recipes in C, Cambridge University Press",
Cambridge
(1992)
(it's now also on the web: http://cftata2.harvard.edu/nr)
Burden and Faires, "Numerical Analysis", PWS Publishing Company,
Boston
(5th ed., 1993)
(This is a , IMHO, good introductionary book in numerical analysis,
It could be used in such a course for computational chemists.)
Wilkinson and Reinsch, "Handbook for Automatic Computation, Vol. II Linear
Algebra", Springer-Verlag, Berlin (1971)
Many have already implemented the algorithms. They are stored in several
packages.
Here are some:
LAPACK: http://www.netlib.org/lapack
EISPACK: http://www.netlib.org/eispack
ARPACK: http://www.caam.rice.edu/~kristyn/parpack_home.html
Thanks to all who responded,
Niels
+----------------------------------------------------------+
| Niels J. van der Laag |
| Student Computational Chemistry |
| Dept. of Physical Chemistry (Solid State NMR) |
| University of Nijmegen |
| Toernooiveld 1, NL-6525 ED Nijmegen, Netherlands |
| phone: ++31-24-3653112 email: nila' at \`solidmr.kun.nl |
| nielsl' at \`sci.kun.nl |
+----------------------------------------------------------+