> For the complete documentation index, see [llms.txt](https://docs.enercalc.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.enercalc.com/e3d-user-manual/analysis/toc161394061/toc161394064.md).

# Solution Convergence

How to address solution convergence and stability problems in frequency analysis.

Due to the iterative nature in the eigen solution, much more computational effort is required (in order to achieve satisfactory convergence) in frequency analysis than in static analysis. Another important difference is solution stability, which is more difficult to achieve in frequency analysis. To ensure that the smallest required eigenvalues and the corresponding eigenvectors have been computed, the program performs a *Sturm* sequence check after the subspace iterations \[Ref 1]. A warning message is given in the solver dialog if some eigen values are missing after the Sturm sequence check. Under some rare circumstances, the solution may become unstable and the solver has to abort the solution process

Several remedies can be used to address the solution instability and solution divergence.

1\). Solve for fewer number of modes.

2\). Use larger number of iteration vectors.

3\). Use 128-bit floating point arithmetics instead of 64-bit floating point arithmetics.

These remedies may be used in tandem. Once again, the 128-bit floating point arithematics is especially effective for solution stability.

The maximum number of subspace iterations is set to 18 by default. If no convergence is achieved at this limit, you should rerun the frequency analysis with a larger maximum number of subspace iterations.


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