An extension of the theory of GLT sequences: sampling on asymptotically uniform grids

Giovanni Barbarino, Carlo Garoni*

*Tämän työn vastaava kirjoittaja

Tutkimustuotos: LehtiartikkeliArticleScientificvertaisarvioitu

2 Sitaatiot (Scopus)

Abstrakti

The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic singular value and spectral distributions of matrices (Formula presented.) arising from virtually any kind of numerical discretization of differential equations (DEs). Indeed, when the mesh fineness parameter n tends to infinity, these matrices (Formula presented.) give rise to a sequence (Formula presented.), which often turns out to be a GLT sequence. In this paper, we provide an extension of the theory of GLT sequences: we show that any sequence of diagonal sampling matrices constructed from asymptotically uniform samples of an almost everywhere continuous function falls in the class of GLT sequences. We also detail a few representative applications of this result in the context of finite difference discretizations of DEs with discontinuous coefficients.

AlkuperäiskieliEnglanti
JulkaisuLINEAR AND MULTILINEAR ALGEBRA
DOI - pysyväislinkit
TilaSähköinen julkaisu (e-pub) ennen painettua julkistusta - 30 kesäk. 2022
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

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