I use Eigen to compute the eigenvalues of symmetric matrices.
The problem is, that sometimes the matrices not nice at all numerically. Because of this, I get NaN among the eigenvalues. I have tested the matrix with maxima and WolframAlpha as well. Maxima would give me two complex and one real eigenvalues, while apparently WolframAlpha is able to compute all three real eigenvalues.
Is there a method or library, that could guarantee the eigenvalues? If not, what can be done in these cases?
For the curious, this is the matrix I've tested: $\begin{bmatrix} 1.4580680&-0.0028459986&0.10822548 \\\\ -0.0028459986&5.5612186 \times 10^{-6}&-0.00012824166 \\\\ 0.10822548&-0.00012824166&1.3172486 \end{bmatrix}$