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# [Analysis] In Eigenvalue Analysis when should Subspace iteration be used and when Lanczos be used?

## Question

In Eigenvalue Analysis when should Subspace iteration be used and when Lanczos be used?

The type of analysis for finding Eigenvalue depends on the various factors as elaborated below.

From Main Menu select Analysis > Analysis Control > Eigenvalue

In Eigenvalue analysis we have two types, Eigen vectors and Ritz vectors. Eigen vector further have sub type.

Subspace Iteration method
When performing Eigenvalue analysis for a finite element system of a large scale (large matrix system), Subspace Iteration method is effectively used.

Lanczos method
Adopted for relatively simpler structure to study the lower modes. Tri-diagonal Matrix is used to perform eigenvalue analysis. Hence the Lanczos method may miss some Eigen pairs. However for practical eigenvalue analysis method, the exact dynamic response has to be obtained which requires the missed eigenvalues to be included. ‘Sturm Sequence Check’ should be selected to check the same.

Ritz Vector
For a model with large degrees of freedom (Say, for model with pile spring supports), Ritz vector method may be more appropriate. Unlike the natural eigenvalue modes, Ritz vectors are load dependent and produce more reliable results in dynamic analyses with relatively fewer modes. The Ritz Vectors are generated reflecting the spatial distribution or the characteristics of the dynamic loading.

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