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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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Speleers, Hendrik (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 ; 2021-007
- Relaterad länk:
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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 this working hypothesis, which is illustrated to be plausible through numerical experiments, we propose an eigensolver for the computation of the eigenvalues of X_n for large n and we provide a theoretical analysis of its convergence. The eigensolver is called matrix-less because it does not operate on the matrix X_n but on a few similar matrices of smaller size combined with an interpolation-extrapolation strategy. Its performance is benchmarked on several numerical examples, with a special focus on matrices arising from the discretization of differential problems.
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