Matrix-Less Eigensolver for Large Structured Matrices

Barbarino, Giovanni (författare)

Claesson, Melker (författare)

Ekström, Sven-Erik (författare)

Department of Information Technology, Uppsala University, 2021
Engelska.
Serie: Technical report / Department of Information Technology, Uppsala University, 1404-3203 ; 2021-007

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Abstract Ämnesord

Stäng

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.

Av författaren/redakt...: Barbarino, Giova ...; Claesson, Melker; Ekström, Sven-Er ...; Garoni, Carlo; Meadon, David; Speleers, Hendri ...

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