Accurate estimation of complex eigenvalues

soikez
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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!
 
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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}##.
 

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