# Large Scale Eigen Value Computation

The numerical solution of large scale algebraic eigen value problems is now available
thanks to new methods and software. A class of methods called Krylov subspace
projection methods is used. The well known Lanczos method is the first
one. The Arnoldi method is a generalization of Lanczos method applied to the
non-symmetric case. A variant of Arnoldi-Lonczos scheme called the Implicitly
Restarted Arnoldi Method ^{1} is a part of public domain software package
called ARPACK which is integrated in Radioss. Restarting is introduced as a way to overcome intractable storage and
computational requirements in the original Arnoldi method. Implicit restarting is a
variant of restarting which may be considered as a truncated form of the powerful
implicitly shifted QR technique that is suitable for large scale problems. It
provides a mean to approximate a few eigen values with user specified properties in
space proportional to the number of eigen values required. The details of the method
are not explained here.

^{1}Sorensen D.C., “Implicit application of polynomial filters in a k-step Arnoldi method”, SIAM J. Matrix Anal. Appl., Vol. 13, pp. 357-385, 1992.