Further generalization of locally Toeplitz sequencesстатья
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Дата последнего поиска статьи во внешних источниках: 28 февраля 2020 г.
Аннотация:Many modern developments of spectral theory of Toeplitz-related matrices are largely motivated by PDE discretizations. However, the existing theory of generalized locally Toeplitz (GLT) sequences assumes that PDEs are defined on a domain which is a parallelepiped, and if not so then at least some diffeomorphic image of it. Here we present two novel results. First, we show that the GLT theory in its present form is insufficient for matrix sequences arising in the case of triangular grids on a triangle. Second, we propose an extension of the GLT classes to cope with this drawback.