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Matrix-Less Eigenso...
Matrix-Less Eigensolver for Large Structured Matrices
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Barbarino, Giovanni (författare)
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Claesson, Melker (författare)
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Ekström, Sven-Erik (författare)
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Garoni, Carlo (författare)
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Meadon, David (författare)
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- Department of Information Technology, Uppsala University, 2021
- Engelska.
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Serie: Technical report / Department of Information Technology, Uppsala University, 1404-3203 ; 2021-005
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https://uu.diva-port... (primary) (Raw object)
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https://urn.kb.se/re...
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Abstract
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- Sequences of structured matrices of increasing size arise in many scientific applications and especially in the numerical discretization of linear differential problems. We assume as a working hypothesis that the eigenvalues of a matrix X_n belonging to a sequence of this kind are given by a regular expansion. Based on the working hypothesis, which is proved to be plausible through numerical experiments, we propose an eigensolver for the computation of the eigenvalues of X_n for large n. The performance of the eigensolver—which is called matrix-less because it does not operate on the matrix X_n—is illustrated on several numerical examples, with a special focus on matrices arising from the discretization of differential problems, and turns out to be quite satisfactory in all cases. In a sense, this is an a posteriori proof of the reasonableness of the working hypothesis as well as a testimony of the fact that the spectra of large structured matrices are much more “regular” than one might expect.
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