# Eigenvalue Methods

### Tips & Tricks

000934 8 December 2014

In RF‑STABILITY, you can perform stability analyses according to four different eigenvalue methods.

#### Method by Lanczos

The eigenvalues are determined directly. In most cases, this algorithm allows you to reach a rapid convergence (see also http://en.wikipedia.org/wiki/Lanczos_algorithm).

#### Roots of the characteristic polynomial

This method is also based on a direct calculation method. For larger structural systems, this method can be faster than the Lanczos method. The main advantage is the calculation accuracy of higher eigenvalues (see also http://en.wikipedia.org/wiki/Characteristic_polynomial).

#### Subspace iteration method

All eigenvalues are determined in one step. The spectrum of the stiffness matrix has a great influence on the duration of calculation. Since the stiffness matrix is stored in the operating memory, this method is not suitable for complex systems. In addition, negative critical load factors cannot be excluded (see also http://en.wikipedia.org/wiki/Krylov_subspace).

#### ICG iteration method

The ‘Incomplete Conjugate Gradient’ method requires little operating memory. Since the eigenvalues are determined one after the other, this requires more computing time for the calculation of small to medium structural systems, in comparison with the direct method. However, the spectrum has no influence on the calculation duration.

The ICG method is suitable for analyses of very large systems with few eigenvalues. This method does not yield any negative critical load factors (see also http://en.wikipedia.org/wiki/Conjugate_gradient_method).