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Beiträge zum Lanczosalgorithmus in endlicher ArithmetikWülling, Wolfgang. Unknown Date (has links) (PDF)
Universiẗat, Diss., 2004--Bielefeld.
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The Anderson Model of Localization: A Challenge for Modern Eigenvalue MethodsElsner, Ulrich, Mehrmann, Volker, Römer, Rudolf A., Schreiber, Michael 09 September 2005 (has links) (PDF)
We present a comparative study of the application of modern eigenvalue algorithms to an eigenvalue problem arising in quantum physics, namely, the computation of a few interior eigenvalues and their associated eigenvectors for the large, sparse, real, symmetric, and indefinite matrices of the Anderson model of localization. We compare the Lanczos algorithm in the 1987 implementation of Cullum and Willoughby with the implicitly restarted Arnoldi method coupled with polynomial and several shift-and-invert convergence accelerators as well as with a sparse hybrid tridiagonalization method. We demonstrate that for our problem the Lanczos implementation is faster and more memory efficient than the other approaches. This seemingly innocuous problem presents a major challenge for all modern eigenvalue algorithms.
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The Anderson Model of Localization: A Challenge for Modern Eigenvalue MethodsElsner, Ulrich, Mehrmann, Volker, Römer, Rudolf A., Schreiber, Michael 09 September 2005 (has links)
We present a comparative study of the application of modern eigenvalue algorithms to an eigenvalue problem arising in quantum physics, namely, the computation of a few interior eigenvalues and their associated eigenvectors for the large, sparse, real, symmetric, and indefinite matrices of the Anderson model of localization. We compare the Lanczos algorithm in the 1987 implementation of Cullum and Willoughby with the implicitly restarted Arnoldi method coupled with polynomial and several shift-and-invert convergence accelerators as well as with a sparse hybrid tridiagonalization method. We demonstrate that for our problem the Lanczos implementation is faster and more memory efficient than the other approaches. This seemingly innocuous problem presents a major challenge for all modern eigenvalue algorithms.
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