Eigenvalue Methods

Tips & Tricks

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

Lanczos method

The eigenvalues are determined directly. With this algorithm, a rapid convergence can usually be achieved (see also https://en.wikipedia.org/wiki/Lanczos_algorithm).

Roots of the characteristic polynomial

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

Subspace iteration method

All eigenvalues are determined in one step. The bandwidth of the stiffness matrix has a great influence on the calculation time. Since the stiffness matrix is stored in the working memory, this method is not suitable for complex systems. In addition, negative critical load factors cannot be excluded (see also http://de.wikipedia.org/wiki/Krylov-Unterraum-Verfahren).

ICG iteration method

The Incomplete Conjugate Gradient method requires little random access memory. Since the eigenvalues are determined one after the other, it requires more computing time for small to medium-sized systems than a direct method. The bandwidth has no influence on the calculation time. The ICG method is suitable for analyzing large systems with few eigenvalues. This method provides no negative critical load factors (see also https://en.wikipedia.org/wiki/Conjugate_gradient_method).


Eigenvalue Lanczos Characteristic polynomial Subspace ICG Critical load factor


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  • Updated 29 October 2020

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Stability analysis according to the eigenvalue method

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