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 ; 2021-005

Relaterad länk:: https://uu.diva-port... (primary) (Raw object); visa fler...; https://urn.kb.se/re...; visa färre...

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 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.

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

Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.