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A well-known numerical problem of the Lanczos diagonalization techniques is the appearance of "spurious" eigenvalues in the course of the iterations. This problem has to do with the loss of orthogonality between the Lanczos states. Since our method requires only a limited number of BL iterations for the convergence of the photoionization cross section, this numerical problem is naturally avoided. It should be noted, however, that with our choice of the starting block as a series of unit vectors corresponding to the 1h1intermediate states, it is straightforward to keethe newly generated Lanczos states orthogonal to the starting block by simply neglecting their corresponding 1h1components.
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