 Fast Toeplitz eigenvalue computations, joining interpolation-extrapolation matrix-less algorithms and simple-loop theory: The preconditioned settingM. Bogoya, S. Serra-Capizzano and P. Vassalos Applied Mathematics and Computation, 2024, vol. 466, issue C Abstract: Under appropriate technical assumptions, the simple-loop theory allows to derive various types of asymptotic expansions for the eigenvalues of Toeplitz matrices Tn(f) generated by a function f. Unfortunately, such a theory is not available in the preconditioning setting, that is for matrices of the form Tn−1(g)Tn(ℓ) with g,ℓ real-valued, g nonnnegative and not identically zero almost everywhere. Independently and under the milder hypothesis that f=ℓ/g is even and monotonic over [0,π], matrix-less algorithms have been developed for the fast eigenvalue computation of large preconditioned matrices of the type above, within a linear complexity in the matrix order: behind the high efficiency of such algorithms there are the expansions as in the case g≡1, combined with the extrapolation idea, and hence we conjecture that the simple-loop theory has to be extended in such a new setting, as the numerics strongly suggest. Keywords: Toeplitz matrix; Spectra; Preconditioned matrix; Asymptotic expansion; Numerical algorithm (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:466:y:2024:i:c:s0096300323006525 DOI: 10.1016/j.amc.2023.128483 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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