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Accurate estimation of complex eigenvalues

  1. Jul 18, 2010 #1
    I use Arnoldi iterative algorithm in order to compute the eigenvalues of a matrix. I know that the eigenvalues are of the form [tex]\lambda(1+j/c)[/tex] and I can totally estimate them. The problem that occurs is that both the range of [tex]\lambda_0[/tex] 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. [tex](10^4,10^6)[/tex], 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 [tex]\lambda=100+0.017j[/tex], the analytically computed eigenvalue is [tex]\lambda=100.1+0.012j[/tex]. 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!
  2. jcsd
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