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.
Implicit application of polynomial filters in a k-step Arnoldi method, SIAM J. Matrix Anal. Appl., Vol. 13, pp. 357-385, 1992.