Accurate estimation of complex eigenvalues

[soikez]

Hello,
I use Arnoldi iterative algorithm in order to compute the eigenvalues of a matrix. I know that the eigenvalues are of the form $$\lambda(1+j/c)$$ and I can totally estimate them. The problem that occurs is that both the range of $$\lambda_0$$ and c is for example [100,1000]. That means that there is a significant difference in the order of real and imaginary part e.g. $$(10^4,10^6)$$, so the algorithm I use defines with more accuracy the real part of the eigenvalue. To be more specific let me give an example. If I estimate an eigenvalue, using python or matlab, as $$\lambda=100+0.017j$$, the analytically computed eigenvalue is $$\lambda=100.1+0.012j$$. This deviation in the imaginary part causes a lot of problems.
Is there any way of normalization in order to exceed this problem of accuracy?

Thanks in advance!

 

[fresh_42]

You could try to describe it as a purely real problem by using the vector space isomorphism $\mathbb{C}\cong \mathbb{R}\oplus \mathbb{R}$.